Thiem earned his first tour-level win in 14 months by downing Emil Ruusuvuori on his Bastad debut, before reaching his first quarter-final of the season by overcoming Roberto Bautista Agut on Thursday.
The Austrian battled to a 7-6 (7-5) 3-6 6-4 victory over the fourth-seeded Bautista Agut, picking up his first top-20 win since beating Novak Djokovic at the ATP Finals in 2020.
Sebastian Baez, who defeated Alejandro Davidovich Fokina in straight sets, awaits in the next round and former world number three Thiem is ready for the task.
"The win against Emil gave me confidence that I can compete against the best players in the world and today against Roberto," said Thiem, the 2020 US Open champion.
"He is always such a tough opponent. I was expecting and hoping it would be a close match. Then when I won the first set in the tie-break I said 'Hey, I can win today.'
"I had the belief until the end of the match and the third set was really good. It is a process. I beat Ruusuvuori and today I beat Bautista Agut.
"Two really top opponents, so if I can beat them I am definitely back. I am into the quarters of a really strong tournament, so I am happy. It is a process, but I am going the right way."
Second seed Andrey Rublev was made to work for his 7-5 4-6 7-6 (7-2) victory over Federico Coria and will meet Laslo Djere, who defeated Marc-Andrea Huesler in straight sets to reach the quarter-finals.
Meanwhile, Auger-Aliassime resumed his match with Jason Kubler in Newport that was suspended due to bad light on Wednesday with a slight advantage but fell to a 4-6 6-3 7-6 (7-4) second-round loss.
That marked a first top-10 victory for Kubler, continuing his fine 2022 season that saw him achieve his best major result at Wimbledon, where he reached the fourth round at the All England Club.
Fourth seed Maxime Cressy is yet to drop his serve at the tournament but needed to survive a first-set scare against fellow American Steve Johnson to triumph 6-7 (3-7) 6-4 6-4.
Second favourite John Isner will meet Cressy in the semi-finals after battling past fifth seed Benjamin Bonzi 6-7 (2-7) 7-6 (8-6) 7-6 (7-5).
When he trailed by a set and 3-0, Cressy's hopes looked almost forlorn, yet the French-American came back to win 2-6 6-3 7-6 (7-3) in two hours and 23 minutes.
The run of six consecutive games in the second set saved Cressy's skin, before he edged a decider against Russian-born Kazakh rival Bublik in which neither man could force a break of serve.
Cressy had a brief injury timeout near the end of the third set, before sweeping through the tie-break.
The grass-court tournament in Newport, Rhode Island, earlier saw Lleyton Hewitt inaugurated to the International Tennis Federation's Hall of Fame, with the former US Open and Wimbledon champion on hand to receive the accolade.
Hewitt won the last ATP title of his career at the Hall of Fame Open in 2014, having lost in the final in the previous two seasons.
The 41-year-old Australian described the Hall of Fame entry on Sunday as "an incredible honour", saying he had previously considered it out of his reach and "for the people that were my idols growing up and the absolute legends of the sport".
Paris-born American Cressy won 7-5 6-7 (3-7) 7-6 (7-4) in a little over two and a half hours, countering 10 double faults with 15 aces on his way to victory.
Rune, the Danish 19-year-old who sits ninth in the world rankings, had won his three previous matches against Cressy, including a second-round clash at the Australian Open last month, but he could not extend that dominance at the indoor event in Montpellier.
It means Cressy faces second seed Sinner, a player he lost to at a low-level tournament in Lexington in 2019, their only past meeting.
Sinner beat 18-year-old French wildcard Arthur Fils in Saturday's first semi-final, ending the teenager's eye-catching run with a 7-5 6-2 victory.
Fils had beaten Richard Gasquet and Roberto Bautista Agut on his way to the last four but found world number 17 Sinner was more than his match.
Last year saw Sinner reach just one ATP final, taking a title on clay in Umag, after making it through to five title matches in the 2021 season.
He had his best year at the grand slams, however, reaching quarter-finals at three of the four majors.
Cressy recognises the threat posed by the Italian, saying in an on-court interview: "Jannik Sinner is an incredible player, just like Holger Rune and everyone else in the tournament. I believe you've just got to bring your 'A' game every time and I'm really looking forward to it."
Competing well in France has been pleasing for Cressy, who is set to climb from 51st in the rankings and into the top 40 on Monday.
"I lived and grew up here, and I'm extremely happy," Cressy said.
Cressy will play his third championship match of the year on Sunday following a 6-2 4-6 6-3 defeat of his fellow American in Newport.
The 25-year-old fired down 22 aces and won 82 per cent of points behind his first serve, breaking three times to move into the final.
Cressy had a stroke of luck for the only break of the deciding set, when he lobbed a shot just over the net and it bounced back onto his side to leave Isner 5-3 down. He then served out the match to end Isner's 10-match winning run in this event.
Bublik sealed his place in the final with a 6-3 6-2 victory over Jason Kubler.
Third seed Bublik did not face a break point and broke the Australian three times, sealing his victory in an hour and nine minutes.
There will be an all-Argentinian final at the Swedish Open between Francisco Cerundolo and Sebastian Baez.
Baez produced an upset, securing his first win against a top-10 opponent with a 6-2 6-4 defeat of second seed Andrey Rublev in Bastad.
Cerundolo got the better of Pablo Carreno Busta 6-3 6-2, ensuring he will face his compatriot for the first time at tour-level.
Djokovic, who is celebrating a record 378th week as world number one, had to rely on a third-set tie-break to finally get over the line, defeating his Czech opponent 6-3 3-6 7-6 (7-1) on Tuesday.
Machac is ranked 130th in the world, but caused Djokovic plenty of problems, earning 10 break points across the match, though he was only able to convert three.
Djokovic had a 4-1 lead in the deciding set before Machac fought back to force a tie-break, but the Australian Open champion ultimately had few problems at 6-6 as he won seven of the eight points played to clinch the win.
"Tomas certainly didn't play like the No. 130 in the world today," Djokovic said of his opponent. "He was giving me all kinds of trouble. But I guess when it mattered, I found another gear."
Djokovic, who is still undefeated in 2023, will face Tallon Griekspoor in the second round.
Elsewhere, fresh off two titles in as many weeks, third seed Daniil Medvedev eased past Matteo Arnaldi 6-4 6-2 to tee up a tie with Alexander Bublik next after his opponent Alexandar Lazarov retired hurt with Bublik leading 6-1 1-0.
Felix Auger-Aliassime defeated Maxime Cressy 7-6 (7-4) 3-6 6-3, but sixth seed Karen Khachanov is out after he was beaten 7-5 6-2 by Botic van de Zandschulp.
The Dutchman will take on Mikael Ymer in the second round after his 6-2 6-3 win against Francesco Passaro, while eighth seed Borna Coric and Dan Evans played just four games before the latter retired hurt.
Christopher O'Connell set up a match against Alexander Zverev in the next round after he overcame Emil Ruusuvuori 7-5 6-4.
For Djokovic, a 10th win in a row came in an absorbing battle with his Paris-born American opponent Maxime Cressy, who displayed a typically aggressive approach on serve, with 15 aces and 10 double faults overall.
Djokovic was strong on his own delivery, however, with the Serbian losing just six points on serve and not facing a break point on his way to a 7-6 (7-1) 6-4 victory.
"I'm happy with the way I played," Djokovic said. "When chances were presented, I was able to use them, even though I did have some missed break points.
"But it was very challenging, first match with a guy who serves extremely well and strong and fast.
"He's comfortable coming to the net. It's nice to see. I think he's the only guy that really comes to the net after every first and second serve. I think it's good for tennis to see that, particularly in these modern times when most of the players are playing from back of the court. He's a very athletic guy.
"It's difficult to play him definitely in these kind of conditions where balls are flying through the court and it's quicker than it was last year. So tough to break.
"But I didn't make too many unforced errors. I'm very pleased with the way I served, with the way I was holding my service games. Just the way I felt, the way I played, it was all positive."
Third seed Ruud ground out a 6-1 7-6 (9-7) victory against Frenchman Richard Gasquet, with the Norwegian saving three of four break points in what proved to be a tightly fought contest.
Mistakes from Gasquet were ultimately costly, the veteran having 10 unforced errors in the second set compared to Ruud's two.
Seventh seed Andrey Rublev was also victorious, the Russian winning 6-2 6-3 against American John Isner, while the British duo of Jack Draper and Dan Evans progressed to the last-32 stage, beating Arthur Rinderknech and Brandon Nakashima respectively.
Three years on from Fritz's breakthrough tour triumph against Sam Querrey – another compatriot – at the same event, the world number 24 was celebrating again in the last tournament before Wimbledon.
Paris-born opponent Cressy had defeated a trio of home hopefuls in succession in Britons Dan Evans, Cameron Norrie and Jack Draper to reach this stage, but Fritz had just too much.
While the Indian Wells Masters champion had not lost a break all week and maintained that record through the decider, he was taken all the way.
"I played about as well as I could possibly play today, and it still came down to the final couple of points," Fritz said afterwards. "It couldn't have been much closer."
That had not appeared likely after an opener in which Fritz's return game dominated 6ft 6in serve-and-volley specialist Cressy, who was broken immediately following a double-fault.
That was one of four in the first set – as many as in three against Draper – as Cressy won just half of his service points, broken again to love.
Yet neither player faced another break point, with a pair of tie-breaks required to settle the title.
The first went the way of Cressy, forcing a decider as a pair of powerful forehands finally broke down Fritz, but he required treatment between sets and had clearly tired by the closing stages.
The latest in a series of Fritz lobs proved beyond Cressy, not that the result should have come as any surprise – improving the champion's career record in deciding tie-breaks to an astonishing 20-3.
World number one Medvedev fought back from a set down to defeat Aslan Karatsev 3-6 6-4 6-2 and advance to a quarter-final against fifth seed Roberto Bautista Agut, who was granted a walkover after Nick Kyrgios pulled out with an abdominal issue.
The Russian got just 48 per cent of his first serves in during a blustery opening set before improving to 68 per cent in the second and controlling the decider as Karatsev struggled with injury.
"It was tough to play [in] rhythm. It felt like many points were just whoever managed to put the ball in the court was going to win the point," Medvedev said of the tricky conditions.
"It was not easy but I'm happy to win because that's the most important [thing].
"Last year was amazing. I played great tennis. Hopefully I can do the same this year. I like it here in Mallorca, so hopefully I can stay as long as possible in the tournament."
Alongside Medvedev and Bautista Agut, Stefanos Tsitsipas is the only other seed left in the draw after he overcame Ilya Ivashka 6-4 6-4.
Denis Shapovalov was a 6-4 6-1 loser against Benjamin Bonzi, Pablo Carreno Busta went down 6-3 6-4 to Antoine Bellier and Sebastian Baez's meeting with Daniel Altmaier ended in a 6-2 2-6 6-4 defeat for the Argentine.
At the Eastbourne International, second seed Sinner suffered a 6-3 3-6 6-3 loss to Tommy Paul as he made his return from a knee injury sustained at the French Open.
World number 13 Sinner remains without a grass-court win in his ATP Tour career, while Paul will next face defending champion Alex de Minaur, who overcame Lorenzo Sonego 7-6 (7-3) 6-2 in a repeat of last year's final.
Jack Draper defeated fourth seed Diego Schwartzman 7-5 7-6 (7-3) to advance to the quarter-finals and Cameron Norrie cruised past Brandon Nakashima in straight sets.
There were also wins for Maxime Cressy, Alexander Bublik and Taylor Fritz.
The three-time grand slam champion was largely in control against his Austrian opponent, hitting nine aces and saving all three break points against his serve, while Thiem could only save one of the three he faced as Murray won 6-3 6-4.
He will now play 14th seed Denis Shapovalov after the Canadian beat Ugo Humbert 7-6 (7-1) 6-3.
The winner of that contest will have a last-16 meeting against the victor of Novak Djokovic and Gael Monfils after the latter eased into the round of 32 to set up a clash with the Serbian.
Monfils defeated wildcard Carlos Gimeno Valero 6-3 6-0 in less than an hour, while Alejandro Davidovich Fokina also advanced with a 7-5 6-3 win against Lloyd Harris.
Dusan Lajovic set up a second-round match against fifth seed Casper Ruud, who defeated Borna Coric 6-3 4-6 6-4, and ninth seed Cameron Norrie will go up against John Isner, the Briton having overcome Soonwoo Kwon 7-5 7-5.
An interesting tie awaits the much-talked about Carlos Alcaraz after Nikoloz Basilashvili beat Fabio Fognini 7-5 6-4, with the Georgian to face the number seven seeded teenager next.
Jannik Sinner, the 10th seed, scraped through a hard-fought encounter against American Tommy Paul 6-7 (4-7) 7-6 (7-4) 6-3, and will play Alex de Minaur next after the Australian beat Pedro Martinez 7-6 (7-2) 1-6 6-3.
Diego Schwartzman will take on Grigor Dimitrov in the second round. The Argentine 13th seed beat Benoit Paire 6-2 6-7 (5-7) 6-1, while Dimitrov overcame Maxime Cressy 6-2 7-6 (7-4).
Finn Ruusuvuori ousted the sixth seed with a 7-5 6-4 victory in Doha with a powerful display.
There were 26 winners from the racket of Ruusuvuori, who had only come out on top in one of his previous eight matches against top-30 opponents.
Ruusuvuori's next assignment will be a meeting with Jiri Lehecka, who saw off qualifier Damir Dzumhur 6-3 7-6 (7-3).
Roberto Bautista Agut, the fifth seed from Spain, saw the back of Marton Fucsovics 7-6 (9-7) 5-7 6-4.
Botic van de Zandschulp, Tallon Griekspoor and Soonwoo Kwon also made it through to round two.
Maxime Cressy had to dig deep to make it out of the first round of the Open 13, beating Geoffrey Blancaneaux 6-3 6-7 (5-7) 7-6 (7-4).
The fifth seed from the United States was joined in the last 16 by David Goffin, who defeated qualifier Lukas Klein 6-2 6-4.
Eighth seed Marc-Andrea Huesler made an early departure after going down in straight sets to Gregoire Barrere in Marseille.
World number 12 Sinner, the 11th seed in the French capital this week, suffered a straight-sets loss to Marc-Andrea Huesler, as did 15th favourite Cilic against Lorenzo Musetti.
Ninth seed Fritz downed Alejandro Davidovich Fokina 7-5 6-2, with Cameron Norrie and Frances Tiafoe also recording straight-sets victories against Miomir Kecmanovic and Lorenzo Sonego respectively.
Victory for Fritz kept the American in the hunt for qualifying for November's ATP Finals in Turin for the first time, needing to reach the final in Paris to overtake Felix Auger-Aliassime or Andrey Rublev.
"Right now I'm just focused on kind of playing myself into the tournament," said Fritz. "I feel like any time this year that I've won a couple of matches in a tournament, then I've done well.
"So I'll just try to focus on these early rounds. Turin is still in the picture, obviously, but there's not much else I really could have done.
"Felix has played really, really well, so he deserves it, but I am going to try to steal his spot this week for sure."
Home favourite Gilles Simon awaits Fritz in the second round at the ATP 1000 event after defeating Andy Murray 4-6 7-5 6-3.
Alexander Bublik and Mikael Ymer played out another three-set battle, with the former triumphing 6-1 6-7 (2-7) 6-4.
Richard Gasquet, Yoshihito Nishioka, Karen Khachanov, Maxime Cressy, Nikoloz Basilashvili and John Isner were the other first-round winners on the opening day in France.
Cressy defeated top seed Holger Rune in the semi-finals but could not repeat that level of performance against Sinner, who is set to rise to 14th in the ATP rankings.
Sinner is the first Italian champion in the history of the tournament, having failed to win a match in his previous two appearances in Montpellier.
He has now collected seven Tour-level titles, with six of those coming on hard courts.
"To be honest, the first key was to hold the serve. In the tie-break I knew he may miss something," said Sinner, who saved all three break points he offered to his American opponent.
"I tried to keep my serve, which I have done, so I am very happy about the first set.
"The second set was a little bit different. I had a couple of good chances but he then served very well.
"I am very happy I broke him here and then I served very well at the end of match."
Sinner claimed two early mini breaks in the first-set tie-break to nose into a 4-0 lead, holding his nerve to win the set at the first time of asking.
A crucial break in the second came in the eighth game, with Sinner clinching victory when Cressy sent a weak volley into the net.
Making his debut at the Mallorca Championships, Tsitsipas sealed his maiden appearance in a grass-court final by cruising past Benjamin Bonzi 6-4 6-4 on Friday.
The world number six has now reached four finals this season, having lost two of the previous three – winning on clay at the Monte Carlo Masters.
It was the second meeting between the pair in as many weeks, with the Greek having also downed Bonzi at the Halle Open.
And Tsitsipas now has a chance to warm up for Wimbledon in winning fashion.
"It was a good match. I am very happy today," Tsitsipas said in his on-court interview. "I have played a final a week before a grand slam before. It was the year I made the final at Roland Garros, in Lyon.
"It worked out pretty well to have that final and consistency of matches. It is different this time. We are talking about a different surface, so we will see."
Tsitsipas has now claimed a tour-leading 39 wins this season, but standing between the 23-year-old and silverware is Spaniard Bautista Agut, who reached a 20th career final by beating Antoine Bellier 7-6 (7-5) 6-2.
Like Tsitsipas, Bautista Agut is aiming for a second title of the season.
At the Eastbourne International, two Americans will vie for the title after Indian Wells Masters champion Taylor Fritz saw off a tough challenge from Alex de Minaur while Maxime Cressy defeated home favourite Jack Draper 7-6 (7-5) 6-7 (2-7) 6-3.
Fritz, who triumphed at Eastbourne in 2019 – similarly against an American, in Sam Querrey – but has found his best form hard to come by of late, also needed three sets to get the better of De Minaur, eventually succeeding 6-1 6-7 (5-7) 6-3.
"It's amazing," Fritz said. "I was having a bit of a rough start coming back from injury to the grass season, and then I came here and the first day I was here I just immediately felt like I was playing good tennis again.
"I just have a lot of confidence being here, obviously great memories, so I'm really excited to come back out and play for the title again."
Three-time grand slam winner Wawrinka, who is the oldest player in the main draw, hit back in the Spanish capital to progress 6-7 (7-3) 6-3 7-6 (7-4).
The 38-year-old won 46 of 54 first-serve points and now has a couple of days to recover before facing fifth seed Rublev, who was handed a bye to the last 32.
Roberto Carballes Baena is also through after defeating David Goffin 6-4 6-4, with Alexander Zverev up next, while Alex Molcan saw off Wu Yibing 6-2 6-4.
There was a shock elsewhere on Wednesday as Diego Schwartzman was downed in straight sets by Hugo Grenier.
