There were no shocks at the Stuttgart Open on Tuesday as Marin Cilic and both seeds advanced.
The grass-court swing got under way with four main-draw matches but little drama in Germany.
One-time Wimbledon finalist Cilic staved off the only two break points he faced against wildcard Rudolf Molleker and seized all five opportunities of his own.
A 7-5 6-3 win was enough to set up a second-round meeting with fifth seed Nikoloz Basilashvili, who beat Dustin Brown in the top half of the draw.
The defeated pair were the only home hopefuls in action, while number six seed Ugo Humbert and Lloyd Harris each also progressed.
Anastasia Pavlyuchenkova fought back to win a pulsating French Open battle with her doubles partner Elena Rybakina and reach an elusive first grand slam semi-final.
A decade after playing in the last eight of a major for the first time at Roland Garros, Pavlyuchenkova finally broke new ground with a hard-fought 6-7 (2-7) 6-2 9-7 victory on Tuesday.
The 29-year-old had lost six grand slam singles quarter-finals but the 31st seed will do battle with surprise package Tamara Zidansek for a place in the championship match in Paris.
Rybakina beat the great Serena Williams to reach the last eight and gave another demonstration of her huge promise, but made 43 unforced errors in an entertaining contest that took two hours and 33 minutes to settle on Court Philippe-Chatrier.
After Kazakh Rybakina claimed the first break for a 3-1 first-set lead with clean striking off both wings, Pavlyuchenkova took a more aggressive approach and that paid off when she got back on serve at 4-3.
Rybakina, the 21st seed, took that setback in her stride, storming into a 5-0 lead after a tactical first-set battle was taken to a tie-break, which ended with Pavlyuchenkova putting a backhand into the net.
Pavlyuchenkova appeared to have missed out on a fourth chance to break in a long sixth game of the second set when she slipped, but looked up while she was sitting on the clay to discover Rybakina had made a mess of a simple smash.
The 29-year-old broke again to wrap up the set and maintained her momentum in the decider, charging into a 2-0 lead - with her backhand firing.
They were back on serve at 4-4 with the nerves jangling following four breaks in five games, both players looking understandably tense but still producing some high-quality tennis.
It was Pavlyuchenkova who claimed the decisive fifth break of a long final set to advance, earning a match point with a rasping forehand winner before her young opponent double-faulted.
Data Slam: A half-century to remember for Pavlyuchenkova
Pavlyuchenkova is making her 50th grand slam main draw appearance and she has marked it with her best run. More proof that persistence pays off.
WINNERS/UNFORCED ERRORS
Pavlyuchenkova – 44/28
Rybakina – 46/43
ACES/DOUBLE FAULTS
Pavlyuchenkova – 5/2
Rybakina – 5/6
BREAK POINTS WON
Pavlyuchenkova– 6/17
Rybakina – 3/7
Simona Halep will play in the inaugural Bad Homburg Open as she aims to return to fitness ahead of defending her Wimbledon title.
World number three and two-time grand slam winner Halep last month withdrew from the French Open after sustaining a calf injury.
The Romanian is targeting a return in time for the grass-court swing and will feature at the new WTA 250 event in Germany.
Designed with preparation for Wimbledon in mind, the Bad Homburg Open will run from June 20-26.
Halep, who has accepted a wildcard, is one of three former Wimbledon winners to be participating, alongside Angelique Kerber and Petra Kvitova.
"I have some good news to share with you," Halep said in a video posted to her official Twitter account.
"I am super excited to announce that I will be playing for the first edition in Bad Homburg and I am looking forward to seeing all of the fans in the stands."
Halep, who has also triumphed at Roland Garros, overcame Serena Williams 6-2 6-2 in the 2019 Wimbledon final.
The grand slam in London did not take place last year due to the coronavirus pandemic.
Tamara Zidansek powered into the French Open semi-finals on Tuesday with a three-set win over Paula Badosa as her remarkable campaign at Roland Garros continued.
The world number 85 was the lowest-ranked player in the quarter-finals, which featured six players never to have reached this stage of a grand slam before, a record in the Open Era.
The first woman representing Slovenia to get to the last eight of a major, Zidansek handled the occasion better as she moved a set and 4-2 ahead on Court Philippe-Chatrier.
Badosa responded with some powerful hitting as her opponent began to falter, but Zidansek summoned up energy reserves when it mattered to clinch a 7-5 4-6 8-6 win in two hours and 26 minutes.
Badosa, the 33rd seed, had never before been beyond the fourth round of a slam but came into the contest with some pedigree at this event, having won the girls' title in 2015.
The Spaniard eased into a 3-0 lead in the opening set, but Zidansek won five of the next six games to take the lead in the match for the first time. Badosa warded off a set point but succumbed to the second as a slice clipped the top of the net.
Badosa had been one of the form players on clay this year, winning in Belgrade last month after reaching the semi-finals in Madrid and Charleston, but the 23-year-old sent a tight forehand into the tramlines to hand Zidansek a 3-1 lead in the second set.
The Slovenian was similarly tentative in the next game, sending a careless shot long to hand back the break to trigger a succession of unsteady service games from both players.
Badosa, who racked up five double faults in the second set, fell 4-2 behind, only to respond with three games in a row, breaking Zidansek to love before levelling the match when a strong forehand forced an error.
Just as she looked in control, Badosa slapped a forehand into the net to hand back a break, and suddenly Zidansek's laser groundstrokes began to find their mark again, a thumping winner moving her 5-4 ahead.
She dug deep to save break points and move 7-6 ahead after the longest game of the match, and one last forehand winner on the second match point was enough to end a gruelling contest and set up a semi-final against the victor of the clash between Elena Rybakina and Anastasia Pavlyuchenkova.
Data Slam: Zidansek on target at critical moments
"I was struggling a little bit but, in the third set, I managed to get my groove," said an emotional Zidansek after an exhausting match.
Her accuracy at the crucial points late in the contest proved decisive. She hit 22 of her 48 winners in the deciding set, helping her to swat away break points before clinching the victory.
WINNERS/UNFORCED ERRORS
Zidansek – 48/39
Badosa – 31/47
ACES/DOUBLE FAULTS
Zidansek – 1/3
Badosa – 2/9
BREAK POINTS WON
Zidansek – 8/13
Badosa – 7/14
Andy Murray could hold the key to Iga Swiatek converting her clay-court mastery to the grass of Wimbledon.
Reigning French Open champion Swiatek has powered through to the quarter-finals this year at Roland Garros, and the 20-year-old looks the player to beat.
But soon attentions will switch from the clay in Paris to the grass of London, and Swiatek feels she could do with some pointers.
As Swiatek wrapped up a straight-sets win over Marta Kostyuk on Monday in Paris, Murray tweeted, "Love watching @iga_swiatek", followed by a heart emoji.
Swiatek responded: "Thank you Sir Andy! Are you by any chance up for a practice? I really need to improve my skills on grass."
Andy Roddick is also a fan of the 20-year-old Polish player, with the former US Open winner responding to Murray's initial tweet by saying: "Agreed. She is awesome."
Murray has been champion twice at Wimbledon, beating Novak Djokovic in 2013 and Milos Raonic in 2016.
It remains to be seen how Swiatek gets on when she heads to the All England Club, having made only one previous appearance there in the women's singles, losing in the first round to Viktorija Golubic two years ago.
She can point to some proven prowess, however, having been girls' champion in 2018.
Swiatek has a French Open campaign to complete before she can seriously begin to think about the grass, with a last-eight clash against Maria Sakkari coming up on Wednesday.
Chris Paul compared the Phoenix Suns to a wrestling tag team after they beat the Denver Nuggets 122-105 in their NBA playoffs semi-final opener.
In front of what Paul described as "crazy" home support, the Suns bossed the second half 65-47 to take first blood in the Western Conference last-four series.
Paul (21 points and 11 assists) and Deandre Ayton (20 points and 10 rebounds) fuelled the second-seeded Suns, who saw all of their starters finish with double-digit points – Devin Booker (21), Mikal Bridges (23) and Jae Crowder (14) making priceless contributions.
With the likes of Cameron Payne and Torrey Craig coming off the bench – the latter having nine points and eight rebounds in under 18 minutes on court – there are good grounds for optimism in the Suns ranks.
Paul said the key to the Suns second-half surge, after slipping 70-60 behind at one point, was "just playing with pace", and a vibrant home atmosphere, with Olympic swimming great Michael Phelps among the crowd.
"They got a nice little lead on us there in the third quarter," he said. "This crowd is crazy. It's crazy. To have the fans in there, the energy, there's nothing like it.
"I told the guys this is why we fought so hard during the regular season to get home-court advantage. I think we truly have that with our fanbase here."
For Denver, MVP favourite Nikola Jokic was limited to 22 points on 10-for-23 shooting, nine rebounds and three assists on the road.
Paul said the Suns have real character as a unit.
"It's fun to be on the team," he said. "It's almost like wrestling and you're tagging in.
"You go out of the game and there's no drop-off, there's just another unit coming in and keeping pressure on you.
"I think that's the benefit of having the team like we have."
The second game in the series takes place on Wednesday, again at the Phoenix Suns Arena.
While Paul praised others, Booker hailed Paul's contribution.
"We felt that energy. We felt that passion behind it," Booker said.
"He just made plays. Not only his scoring ability but getting everybody else involved. That's been the story of the season for us, following him in that regard."
The in-form Boston Red Sox extended their winning streak to five games with a 5-3 victory over the Miami Marlins.
Boston stayed hot on Monday, using a three-run fourth inning to take down Miami following a first three-game sweep of the New York Yankees in the Bronx since June 2011.
Christian Arroyo hit a two-run single in the fourth, while Red Sox team-mate Alex Verdugo added an RBI double and two hits in the makeup game from May 30.
"I'm a big believer that when you come from that series [in New York], sometimes you have letdowns," Boston manager Alex Cora said. "To win [tonight] meant a lot. They grinded, they made pitches."
The Red Sox (37-23) are only a half-game behind the idle Tampa Bay Rays (38-23) for the American League (AL) East lead.
Angels soar thanks to Stassi
Max Stassi homered and drove in three runs to lead the Los Angeles Angels past the Kansas City Royals 8-3.
Kowar roughed up in debut appearance
Kansas City's Jackson Kowar made his major league debut but it did not go according to plan. Kowar was removed after allowing four runs on three hits and two walks in just 0.2 innings. The 24-year-old became the second AL starter in the expansion era to give up four or more runs in less than an inning in his MLB bow.
Monster Manny
San Diego Padres star Manny Machado capped a 9-4 win over the Chicago Cubs with a home run in the eighth inning. Padres team-mate Brian O'Grady also homered in the third.
Monday's results
San Diego Padres 9-4 Chicago Cubs
Boston Red Sox 5-3 Miami Marlins
Los Angeles Angels 8-3 Kansas City Royals
Dodgers at Pirates
After back-to-back defeats, World Series champions the Los Angeles Dodgers (34-25) visit the lowly Pittsburgh Pirates (23-35) on Tuesday. The Dodgers will send Walker Buehler to the mound, while the Pirates counter with JT Brubaker.
Brooklyn Nets superstar Kevin Durant attempted to play down the team's obliteration of the Milwaukee Bucks, insisting "we just did what we were supposed to do".
Durant put on a show in the absence of fellow former MVP James Harden (hamstring) with 32 points in three quarters as the merciless Nets earned a commanding 2-0 lead in the Eastern Conference semi-finals on Monday.
The second-seeded Nets – who defeated Milwaukee in three consecutive home games for the first time since 2006-09 – led by as much as 49 points in their most lopsided postseason victory in franchise history.
Brooklyn, eyeing a maiden championship, became the first team since the 1987 Los Angeles Lakers to score at least 115 points in each of their last six playoff games.
The Nets – who set a franchise postseason record with 21 three-pointers – became the first team in playoff history to have an MVP winner (Harden) miss the game and yet still win by 35-plus points, according to Stats Perform.
"I liked our attention to detail," Durant said afterwards. "We didn't get a lot of plays perfect, but we made second and third efforts.
"They didn't destroy us on offensive rebounds so that showed we were boxing out.
"For the most part, we just did what we were supposed to do at home. Now we have to see if this game can travel on the road for us, and we gotta stay locked in."
Game 3 will be in Milwaukee on Thursday and Durant added: "I feel like that's every team's mentality if you got home court.
"We know how important Game 3's are and we know that their crowd is going to be in it from the second we get on the floor for warm-ups and we know their guys they play better and more comfortable when they sleep in their own beds and got their same routines at home. So we got our work cut out for us but we're looking forward to it."
Kyrie Irving had 22 points of his own at home to the third-seeded Bucks in Brooklyn.
''I think we're capable of greatness every single night,'' Irving said.
On the offensive unselfishness of the Nets, Irving added: "That's how you play the game the right way. You know, we are very special individually but the selflessness which you're referring to is really what creates the difference.
"Defense is going to win us games down the stretch, but offensively playing the right way and trusting one another is — those little plays that make the difference towards the end of the game where we don't have to go for it all right then and there wherever the score is.
"So, like I said, this team, we've grown so much and we continue to do so. Obviously, we're missing James. You know, and we're just filling in the pieces for him."
Giannis Antetokounmpo is continuing to believe, despite the Milwaukee Bucks falling into a 2-0 hole following a demoralising defeat to the Brooklyn Nets in Game 2 of the Eastern Conference semi-finals.
Antetokounmpo and the Bucks were no match for the star-studded and James Harden-less Nets, who showed no mercy in a devastating 125-86 victory in the NBA playoffs on Monday.
The third-seeded Bucks trailed by as much as 49 points in a forgettable game in Brooklyn, where two-time reigning MVP Antetokounmpo finished with 18 points on eight-for-15 shooting and 11 rebounds.
Antetokounmpo and the bruised Bucks will return to Milwaukee for Game 3 on Thursday, but their superstar remains upbeat in pursuit of the franchise's first championship since 1971.
"It's easy," Antetokounmpo replied when asked how he could prevent his team-mates from losing confidence. "That's what I do.
"I don't get too high, I don't get too low. After the Miami series, we were up 4-0, and coming to this series, I wasn't high.
"Now that we're down 2-0, I'm not low. I'm just going to keep doing what I'm doing, keep trusting my work, keep trusting my team-mates, keep believing in the team, keep believing in the habits we've built all year, and hopefully in Game 3 we get a win."
The Bucks were easily beaten by the Miami Heat in the second round of last season's playoffs, while Milwaukee are yet to progress beyond the Eastern Conference semi-finals (2019, 2001, 1986, 1984, 1983) since 1973-74.
"It's an opportunity," Antetokounmpo said. "At the end of the day, we have to take care of business, and take it a game at a time. I do not want to hear we got to win two at home.
"We got to win one at home. We've got to win the first game. We've got to get Game 3 and try to give everything we can to get that one, and then Game 4 try to do the same thing. But we have to focus on Game 3 right now."
Giannis Antetokounmpo and the Milwaukee Bucks had no answers as Kevin Durant guided the Brooklyn Nets to a brutal 125-186 victory in Game 2 of the Eastern Conference semi-finals.
Harden sat out due to hamstring tightness, but the star-studded Nets still made light work of the Bucks in Monday's blow-out win for a commanding 2-0 lead in the NBA playoffs.
Durant put on a show against two-time reigning MVP Antetokounmpo and the visiting Bucks, posting 32 points in three quarters while Kyrie Irving added 22 points.
The second-seeded Nets – who defeated Milwaukee in three consecutive home games for the first time since 2006-09 – led by as much as 49 points in their most lopsided postseason victory in franchise history.
Brooklyn, eyeing a maiden championship, became the first team since the 1987 Los Angeles Lakers to score at least 115 points in each of their last six playoff games.
The Nets – who set a franchise postseason record with 21 three-pointers – became the first team in playoff history to have an MVP winner (Harden) miss the game and yet still win by 35-plus points, according to Stats Perform.
Antetokounmpo had a double-double of 18 points and 11 rebounds for Milwaukee, but the Bucks superstar was far from efficient.
Milwaukee's Antetokounmpo was eight-for-15 shooting, while he missed all three of his attempts from beyond the arc and had three turnovers.
Khris Middleton finished with 17 points, however, he was seven-for-20 shooting from the field, having made only three of his eight three-pointers.
In the west, the Phoenix Suns opened their semi-final matchup with a 122-105 win at home to the Denver Nuggets.
Chris Paul (21 points and 11 assists) and Deandre Ayton (20 points and 10 rebounds) fuelled the second-seeded Suns, who saw all of their starters finish with double-digit points – Devin Booker (21), Mikal Bridges (23) and Jae Crowder (14).
The Suns took control in the second half, outscoring the third-ranked Nuggets 65-47 in Game 1.
MVP favourite and Nuggets star Nikola Jokic was limited to just 22 points on 10-for-23 shooting, nine rebounds and three assists on the road.
Clippers at Jazz
The Los Angeles Clippers and top-ranked Utah Jazz will open their Western Conference second-round series on Tuesday. In the east, the Philadelphia 76ers will be looking to bounce back in Game 2 at home to the Atlanta Hawks.
The NBA fined Daryl Morey and the Philadelphia 76ers $75,000 each for a tweet regarding Golden State Warriors superstar Stephen Curry.
Philadelphia president of basketball operations Morey violated the league's anti-tampering rules following a tweet last week, while the 76ers were also fined for his conduct.
Morey tweeted "join 'em" with a picture of an Instagram post by Curry regarding his brother and 76ers guard Seth Curry.
Stephen Curry posted via social media after his brother scored a playoff career-high 30 points in Game 5 of Eastern Conference first-round series against Washington Wizards.
Golden State's Curry is not scheduled to be an unrestricted free agent until after next season having signed a then-record $201million, five-year contract in July 2017.
Curry would be 38 at the end of such a deal, but the two-time MVP has shown no signs of slowing down after averaging a career-high 32.0 points during the regular season to become the oldest NBA scoring champion since a 35-year-old Michael Jordan accomplished the feat in 1997-98.
Philadelphia 76ers head coach Doc Rivers issued a warning about Joel Embiid's health despite his injury return, insisting "we're still not out of the woods" as the Eastern Conference top seeds look to bounce back against the Atlanta Hawks.
Embiid returned from a meniscus tear in Philadelphia's shock 128-124 loss at home to the fifth-seeded Atlanta Hawks in the NBA Eastern Conference semi-final opener on Sunday.
MVP finalist Embiid sat out the series-clinching win over the Washington Wizards due to the right knee injury, which he sustained in Game 4 of the opening-round matchup.
The 76ers outscored the Wizards by 31.6 points per 100 possessions with Embiid on the court but were outscored by 7.5 points per 100 possessions when he went to the bench (excluding Game 5), according to Stats Perform.
Embiid led all scorers with 39 points on 12-for-21 shooting, while he also had nine rebounds, four assists, three blocks and a steal against the visiting Hawks in Philadelphia.
Gearing up for Tuesday's Game 2 at Wells Fargo Center, Rivers provided an update on All-Star Embiid following Monday's practice, telling reporters: "He looked pretty good.
"Obviously, we didn't do much today, but just my observation, without being a real medical doctor, is that he looked pretty good. We were happy with everything."
Embiid has been averaging 27.0 points, 7.2 rebounds and 2.8 assists per game in this season's playoffs, while he boasts career highs in field-goal percentage (61.6), three-point percentage (43.8) and free-throw percentage (90.5).
In 2020-21, Embiid has averaged a career-high 28.5 points, 10.6 rebounds and 2.8 assists per game.
"I think we always have to worry," Rivers added. "I don't think we're out of the woods, I'll put it that way. I think after each game he's gonna be evaluated for a while.
"I don't know how long that lasts, there may be three or four or five games, but we're still not out of the woods, I guess, would be the best way to describe it."
The 76ers were blown away by Trae Young and the Hawks, who led 75-54 at half-time. According to Stats Perform, that is the highest first-half point total by a road team in a postseason series opener in history.
Young had 25 of his 35 points in the first half as the Hawks outscored the 76ers 42-27 in the first period.
Philadelphia's Ben Simmons (17 points and 10 assists) had a double-double but it was a disappointing outing for the 76ers, who are eyeing their first championship since 1983.
However, All-Star Simmons remains upbeat, adding: "The confidence has always been there. I think it's just more so we got to lock in and be ready for whoever comes in the building because it's not going to be easy.
"It's the playoffs and this is a good team we're facing right now. They play the right way. They share the ball, and they play together. We got to come together and play the right way."
New York Knicks head coach Tom Thibodeau has been named the 2020-21 NBA Coach of the Year, it was announced on Monday.
Thibodeau was recognised for leading the Knicks to their first playoff berth since 2013 in his first season in charge – the franchise lost to the Atlanta Hawks in the Eastern Conference first round.
The 63-year-old received 43 first-place votes and 351 total points to beat Phoenix Suns counterpart Monty Williams to his second Coach of the Year award, while Utah Jazz coach Quin Snyder finished third.
Thibodeau also won the Coach of the Year award in his first season as a head coach with the Chicago Bulls in 2010-11.
The veteran is now the first person to be named NBA Coach of the Year in his first season as a head coach with two different franchises.
Thibodeau is also the 10th head coach to win the NBA Coach of the Year Award more than once and the eighth to do it with multiple franchises, while he is the third head coach to be selected as NBA Coach of the Year with the Knicks, joining Red Holzman (1969-70) and Pat Riley (1992-93).
Led by Thibodeau, the Knicks ended the regular season tied for the fourth-best record in the Eastern Conference (41-31) as Julius Randle earned All-Star selection for the first time in his career and the Most Improved Player award.
The Knicks starred defensively throughout the season – leading the NBA in points allowed (104.7), opponents' field-goal percentage (44.0) and three-point percentage (33.7), while New York ranked fourth in defensive rating (107.8).
Facing Rafael Nadal at the French Open is arguably the toughest challenge in sport, such is the King of Clay's incredible record at Roland Garros and, for Diego Schwartzman, forgetting about the 13-time champion and his reputation will be half the battle when he faces him in Wednesday's quarter-final.
Schwartzman is enjoying another excellent run at Roland Garros, having reached the semi-finals last year only to be defeated by Nadal in their 11th career meeting.
The Argentinian saw off Jan-Lennard Struff in straight sets on Monday before Nadal recovered from a slow start to beat Jannik Sinner in three and set up a reunion in the last eight.
They are the only two players remaining in the draw who are yet to drop a set.
Schwartzman has a 1-10 record against Nadal but has the distinction of having beaten the Spaniard on clay, doing so in Rome in 2020.
And he took a set off Nadal in their first clash at Roland Garros back in 2018, though he could not do the same last year.
Asked about the prospect of a four or five-hour match with Nadal, Schwartzman told a media conference: "I think at the beginning of every match against Rafa, you have to walk on the court thinking to win the match, to have opportunities, to get opportunities, and think about something else and not think about Rafa on the other side of the net.
"If you think about the four, five hours you are going to play, if you think about everything about Rafa in Roland Garros, he's very difficult to play.
"You know, you have to go on court, think about the tactics, think about how to play your best game.
"It's Rafa and you never know what is going to happen, and everyone knows that it's going to be very difficult.
"Playing against Rafa in these kind of tournaments, it's always, I mean, a good step, a good time to know how good are you playing. It's always a good challenge.
"I want to be there one more time. I beat him one time, so is not the same thing. I know we played two times here were good matches, and now let's see what happens. I have to enjoy today, day free tomorrow, and let's see what happens on Wednesday."
Nadal heads into the contest content with his overall performance against Sinner, who failed to serve for the first set and could not produce a turnaround in the second despite fighting from 4-0 down to get back on serve at 4-3.
"I think I started the first two games playing great. Then I had a bad game with 2-0 and with the wind helping, so that was a big mistake. Then I started to play too much against his backhand and too far from the baseline. So then I give him the chance to be inside the court and to have the control of the point from inside," said Nadal.
"From that position he's dangerous. I was a little bit farther every time, no, from the baseline. Then I was able to have the break back in the 5-4 with the wind helping. I know that was a chance. So it was important to hold my serve with the 5-3 against the wind.
"Then with the 5-4, you know that you can have your chances. So that's what happened. I won that game. I had the break. Then I play a solid game with my serve.
"Then from that moment to 7-5, 4-0 I think I played very good level of tennis. Then again, couple of mistakes and he played well, honestly. Four-three until that moment to the
end of the match I think I played great."
Defending champion Iga Swiatek overcame a strong challenge from Marta Kostyuk to reach the French Open quarter-finals.
Swiatek is the only top-10 player in the last eight of the women's draw at Roland Garros after beating the 18-year-old Kostyuk 6-3 6-4 on Monday.
Playing her first night match on Court Philippe-Chatrier, Swiatek came from a break down in a thrilling first set and went on to book a meeting with Maria Sakkari – conqueror of last year's runner-up Sofia Kenin.
Eighth seed Swiatek has won 22 consecutive sets at the Paris grand slam and is a strong favourite to win back-to-back titles.
Swiatek, who won a marathon doubles match in combination with Bethanie Mattek-Sands on Sunday, was 2-1 down in the opening set as world number 81 Kostyuk was rewarded for her positive approach.
The 20-year-old Pole responded like a champion, though, breaking back immediately and again after fending off two break points to take a 4-3 lead.
Swiatek, demonstrating her great power and precision, served out the opening set and went a break up at 2-1 in the second, but Kostyuk – playing at this stage of a grand slam for the first time –was not finished yet.
The teenager defended brilliantly and showed great speed over the court as she broke back to level at 2-2 when Swiatek netted a backhand.
Yet Swiatek edged back in front when Kostyuk put a backhand of her own into the net and sealed victory with a magnificent winner – her 24th of an entertaining match.
Luka Doncic appeared to confirm he would be signing a supermax contract extension with the Dallas Mavericks following their NBA playoff exit.
The Mavs were eliminated from the postseason with Sunday's Game 7 defeat to the Los Angeles Clippers, despite another outstanding series from Doncic.
The Slovenian has played in only two playoff series – both defeats against the Clippers – but has quickly established himself as one of the league's elite offensive players.
Doncic scored 35.7 points per game across the seven games, improving his career postseason average to 33.5.
That is the best mark of any player to appear in 13 or more playoff games, passing Michael Jordan's 33.4.
Jordan is one of only three men since 1963 to outscore Doncic across the first 13 games of his playoff career, with the Mavs superstar matching Kareem Abdul-Jabbar's 436 points.
Dallas will pursue an extension to keep Doncic on the team long term, and he replied to questions about an imminent supermax deal: "I think you know the answer."
Doncic is still playing on the four-year rookie contract he signed after the Mavs traded with the Atlanta Hawks on draft night in 2018.
The 22-year-old is set to earn $10.2million in the coming season, but Dallas are expected to make him an offer that would then exceed $200m across the next five years.
Doncic, who averages 25.7 points in the regular season, was the Rookie of the Year in 2018-19 and made the All-NBA First Team last year. He will likely be included in the same selection for 2020-21.
American duo Caty McNally and Caroline Dolehide bounced back from their French Open woe with victories at the Nottingham Open as their grass-court seasons began.
McNally and Dolehide both failed to progress through qualifying at the ongoing grand slam in Paris, but they recovered to make successful starts to their campaign at the WTA 250 event on Monday.
World number 36 McNally – on the day her doubles partner Coco Gauff reached the last eight in the singles at Roland Garros – won 6-4 6-3 against India's Ankita Raina, saving five of the six break points she faced.
McNally – beaten by Gauff in the French Open junior final in 2018 – will now cheer the 17-year-old on from afar while she herself looks to make further progress in England.
Dolehide conceded just one break point as she won by the same scoreline against Giulia Gatto-Monticone, while home hope Harriet Dart beat compatriot Emma Raducanu in straight sets.
Australian pair Lizette Cabrera and Arina Rodionova both beat Chinese opponents, seeing off Wang Yafan and Wang Xinyu respectively.
Number one seed Johanna Konta will begin her campaign on Tuesday against Lesley Pattinama Kerkhove.
The Dominican Republic’s good run of form was halted Sunday when they lost to Russia at the Volleyball Nation’s League in Italy.
Rafael Nadal continued on his serene path to a 14th French Open title by seeing off Jannik Sinner in straight sets.
Having seen Italian compatriot Lorenzo Musetti take Novak Djokovic to five sets earlier on Court Philippe-Chatrier, Sinner made a strong start against the King of Clay.
However, whereas Musetti took two sets from the world number one before being outpunched by Djokovic, Sinner was swiftly reeled back in after spurning a chance to win the first set.
The 19-year-old's spirited efforts were undermined by 40 unforced errors, offering Nadal far too many opportunities to press home the gulf in class and experience in a 7-5 6-3 6-0 win.
Nadal held to love in his first service game and then immediately broke Sinner. However, he was uncharacteristically sloppy across his next two service games, sending down three double faults, as Sinner reversed the tide to surge into a 4-2 lead.
Yet the teenager crumbled as he failed to serve out the set, surrendering a break to love with a double fault.
Then tasked with serving to stay in the set, Sinner had no answer for Nadal, who was now in full flow, an exquisite drop shot bringing up three set points. Sinner saved one, but Nadal's defence forced him into a forehand error that handed the Spaniard his 33rd consecutive set at Roland Garros.
A scorching cross-court backhand saw Nadal craft an early break in the second and he seemingly had a stranglehold on the contest after going 4-0 up.
Sinner surprisingly rattled off the next three games to get back on serve, only to instantly cede the advantage back to Nadal, who subsequently wrapped up the second set with a powerful serve down the middle.
And there was no fightback from Sinner in the third as Nadal coasted to a last-eight clash with Diego Schwartzman, who won earlier against Jan-Lennard Struff.
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