French qualifier Barrere and US veteran Isner were forced indoors by the adverse weather threat in New Zealand, with the entire Tuesday schedule taking place on inside courts and without spectators.
Despite Isner rifling down 28 aces to move 10 away from becoming the first man to post 14,000 in ATP tour and grand slam events, Barrere stuck with him and pulled off a 6-7 (3-7) 7-6 (7-5) 6-3 victory.
He snatched the only break of the match in game eight of the deciding set, before serving out for victory, with the world number 88 firing down 10 aces himself across the contest.
Argentine seventh seed Sebastian Baez also fell at the last-32 stage, bowing out 7-6 (7-1) 6-1 to American wildcard Ben Shelton.
Serbian Laslo Djere set up a second-round clash with top seed Casper Ruud by edging out Spain's Jaume Munar 3-6 6-1 7-6 (7-4), while Czech Jiri Lehecka will face second seed Cameron Norrie next after sinking Brazilian fellow qualifier Thiago Monteiro 6-3 7-5.
Ruud and Norrie received first-round byes.
At Adelaide International 2, American eighth seed Tommy Paul battled past Australian Christopher O'Connell 6-4 7-5, setting up an appetising second-round clash with Britain's Jack Draper, who won through on Monday.
There was a home success for the Australian crowd to cheer, though, as qualifier John Millman, who beat Roger Federer at the 2018 US Open, this time dug deep for a 4-6 6-3 7-6 (8-6) win against Spain's Albert Ramos-Vinolas.
Top seed Berrettini, ranked nine in the world, has not dropped a set all week.
His impressive run has seen him defeat home hopes Andy Murray and Dan Evans, with one more Briton in the shape of Norrie left to see off in his bid for glory.
Berrettini ensured he will be in the final by claiming a 6-4 6-4 triumph over fourth seed Alex de Minaur in the semi-final on Saturday.
The Italian dropped just four of his 36 points on first-serve and sent down eight aces, with De Minaur only able to force one break point in the entire contest, which he did not take.
"[Making the final] was the goal of the week and now I have one more step," said Berrettini.
"It is a great achievement, especially for the history of this tournament. I am really happy because to beat Alex, I had to play my best tennis."
Berrettini has four tour titles to his name, though this would be his first at ATP 500 level or above.
Victory would also represent the biggest win of Norrie's career – he has lost each of his three previous finals, all at ATP 250 level.
Norrie impressively eliminated Denis Shapovalov to reach the showpiece, beating the Canadian 7-5 6-3.
Shapovalov had earlier finished off a 6-3 6-4 quarter-final win over Frances Tiafoe, a match that could not be completed on Friday due to fading light.
But the second seed could not muster up another victory against a fresher Norrie.
At the Halle Open, Andrey Rublev reached his eighth final since the start of 2020, though his first on a grass court.
Rublev dropped his first set of the week but ultimately prevailed with a 6-1 3-6 6-3 semi-final victory over Nikoloz Basilashvili.
The Russian has won his last four finals at ATP 500 level and will seek a fifth on Sunday.
"It's my first final on grass and in Halle," he said. "I think I can play on every surface and I will try my best again.
"I had good opportunities to break Basilashvili in the second set, some quite easy forehands and I stressed a little showing my emotions.
"I then came back and stayed calm, until the last game. But I won."
Rublev will take on unseeded Ugo Humbert, who held his nerve to edge a thriller against Felix Auger-Aliassime, winning 6-4 3-6 7-6 (7-5).
Humbert beat Alexander Zverev earlier in the week and has had to win a deciding set in all four rounds, while the beaten Auger-Aliassime had previously seen off Roger Federer as part of a dramatic event.
Frenchman Humbert won each of his first two career finals, which both took place last year in ATP 250 events.
The Italian returned from injury in emphatic fashion at the Stuttgart Open, defeating Andy Murray in the final, before heading to Queen's ahead of the start of the third major of the year.
Berrettini had little trouble negotiating his way through to Sunday's showpiece, dropping just one set throughout the tournament to set up a meeting with Filip Krajinovic.
And despite having to battle in the first set, Berrettini triumphed 7-5 6-4 to retain the title he won last year.
The 26-year-old had an early break cancelled out by Krajinovic but got a crucial second break to take the first set.
A tentative opening followed in the second set, yet Berrettini's patience paid off when he broke in the fifth game and he was able to serve out the victory.
That signified Berrettini's ninth straight win, all on grass, after a three-month injury lay-off.
Berrettini is the first player in the Open Era to win titles in each of his first two appearances at Queen's, and is the eighth repeat champion at the tournament – the other seven players to have achieved that feat are all former world number ones.
"I arrived to Stuttgart, and I wasn't feeling great, I wasn't hitting the ball the way I want it that way I used to do, and I was like 'guys I think it's going be tough' and then it went pretty well," he said after the win," Berrettini said.
"I mean I guess I'm Italian, I'm always complaining!"
Berrettini has also advanced to the final in all four of his past grass-court events, with his only defeat coming against Novak Djokovic at Wimbledon last year.
The world number 10 will now look to go one better this time around at The All England Club.
After a delay of more than four hours because of rain in London, Berrettini overcame Evans 7-6 (7-5) 6-3 to reach his third ATP grass-court semi-final.
The Italian hit 13 aces and won 81 per cent of his first-serve points against Evans to set up a last-four clash with Alex de Minaur.
Berrettini improved his win-loss record to 24-6 for the season and laid out his ambition to walk away from the tournament with the trophy.
"I didn't serve that well, but I was returning well and I just played better in the last few points of the tie-break," he said.
"After that, I felt more confident. The conditions were really tough, windy and cold, so I took time to adapt a little bit. I am pretty happy with my performance.
"The court condition was really good. I expected slippery conditions, but it was like yesterday.
"I came here to win the tournament, that is my goal. Now I am two steps away. I am happy with the way I am playing, and my mental attitude is really good."
Up next for Berrettini is Australian De Minaur, who came from behind to defeat Marin Cilic 3-6 6-3 6-4.
The 22-year-old won 73 per cent (22/30) of his second-serve points and saved six of the seven break points he faced as he moved to 16-12 for the season.
In the battle of the British players, Cameron Norrie beat Jack Draper 6-3 6-3, while Denis Shapovalov was leading Frances Tiafoe 6-3 when their match was suspended due to fading light. They will resume on Saturday.
At the Halle Open, Andrey Rublev reached his sixth ATP Tour semi-final of the year thanks to a 7-6 (7-4) 6-2 win over 2011 champion Philipp Kohlschreiber.
"I am happy with my performance to reach the semi-finals for the first time," Rublev said. "The first set was really tough. He was 3-0 up in the tie-break and I came back, which was the key.
"After the first set, I think he mentally went down and I was pumped up. I hit a couple of good returns in the first game of the second set."
Russian Rublev will face Nikoloz Basilashvili in the last four after the Georgian defeated Lloyd Harris 6-4 7-6 (7-5).
In the day's other quarter-finals, Felix Auger-Aliassime beat Marcos Giron 6-3 6-2 and Ugo Humbert overcame Sebastian Korda 6-2 6-7 (5-7) 6-4.
Borges created a remarkable 20 break points, converting only five but still comfortable against his 61st-ranked opponent.
That sets up a clash with number one seed Alcaraz, who beat Pablo Carreno Busta in the 2022 final.
Ben Shelton's 7-5 6-4 success over countryman Mackenzie McDonald means he will take on Casper Ruud, while Bernabe Zapata Miralles will play Roberto Bautista Agut in an all-Spanish second-round affair after earning a routine 6-2 6-2 win over unfancied Attila Balazs.
Meanwhile, Emil Ruusuvuori beat Alexander Bublik in Barcelona for a second straight year to set up a second-round meeting with fifth seed Frances Tiafoe.
At the BMW Open in Munich, 2022 winner Holger Rune will open his defence against Yannick Hanfmann after the German battled from a set down to beat Thiago Monteiro 6-7 (3-7) 7-6 (7-5) 6-2.
Marcos Giron reached the second round with a 6-1 5-7 6-2 victory over Roberto Carballes Baene.
World number 16 Carreno Busta, the seventh seed at the ATP 500 event in the Netherlands, took the first set with ease but fell to a 2-6 7-6 (7-2) 6-2 defeat against Frenchman Gasquet.
Veteran Gasquet, ranked 45th in the world, will next meet Stan Wawrinka after the Swiss overcame Alexander Bublik in dominant fashion with a 7-6 (7-5) 6-4 triumph.
Grigor Dimitrov recorded a 6-1 6-3 victory over Aslan Karatsev in just 59 minutes to set up a potential second-round tie with fifth seed Hubert Hurkacz, who must first get past Roberto Bautista Agut.
Qualifier Gregoire Barrere was another straight-sets winner, defeating David Goffin 6-0 7-6 (7-3).
The Frenchman, who is ranked 71st in the world, could meet third seed Felix Auger-Aliassime in the next round if the Canadian overcomes Italy's Lorenzo Sonego.
Spanish second seed Carreno Busta wrapped up a convincing 6-2 6-4 win over Krajinovic of Serbia in one hour and 23 minutes.
Krajinovic, who beat Stefanos Tsitsipas in the quarter-finals, had no answer to Carreno Busta's serve as he won 81 per cent (21/26) of his first-service points.
Carreno Busta broke Krajinovic's serve twice in the first set before he served out.
Krajinovic showed more fight in the second set, but he was unable to create a break chance, and when he offered one to Carreno Busta his opponent seized it.
The victory gave world number 13 Carreno Busta, who did not drop a set in the tournament, his 17th win on clay this season.
It was a tremendous week in Acapulco for the Australian, having eliminated world number 10 Holger Rune in the semi-final en route to his seventh title overall, with the first six all at the ATP 250 level.
Against Paul, De Minaur blew a pair of break points in the opening set, and then gave up the break in the very next game, allowing the American to serve things out safely to take the first frame.
But mistakes started to creep into Paul's game the longer the match went. After landing 75 per cent of his first serves fair in the opener and avoiding any double-faults, Paul's first serve percentage dropped to 46 in the second, and he committed a pair of doubles.
He committed another two double-faults in the decider to hand De Minaur the early break, and his play from the baseline also deteriorated, hitting just six winners to go with 14 unforced errors.
Known for his resilience, De Minaur had to save five break points to hold serve in the opening game of the third set, but he held his nerve, and churned out five consecutive games as Paul ran out of gas.
The 500 ranking points will see the Aussie climb to 18th in the world, with his career-best mark of 15th now within reach.
Meanwhile, the fairytale continued for Nicolas Jarry at the Chile Open, with the Santiago-born talent electrifying his home crowd with a 1-6 7-6 (7-4) 6-1 semi-final victory over Jaume Munar.
Jarry will get a chance for the second ATP title of his career, and the first since 2019, when he meets Tomas Martin Etcheverry in the final.
Etcheverry emerged victorious 7-5 6-3 in an all-Argentine showdown against third seed Sebastian Baez, earning his first final appearance at this level.
It was a tremendous week in Acapulco for the Australian, having eliminated world number 10 Holger Rune in the semi-final en route to his seventh title overall, with the first six all at the ATP 250 level.
Against Paul, De Minaur blew a pair of break points in the opening set, and then gave up the break in the very next game, allowing the American to serve things out safely to take the first frame.
But mistakes started to creep into Paul's game the longer the match went. After landing 75 per cent of his first serves fair in the opener and avoiding any double-faults, Paul's first serve percentage dropped to 46 in the second, and he committed a pair of doubles.
He committed another two double-faults in the decider to hand De Minaur the early break, and his play from the baseline also deteriorated, hitting just six winners to go with 14 unforced errors.
Known for his resilience, De Minaur had to save five break points to hold serve in the opening game of the third set, but he held his nerve, and churned out five consecutive games as Paul ran out of gas.
The 500 ranking points will see the Aussie climb to 18th in the world, with his career-best mark of 15th now within reach.
Meanwhile, the fairytale continued for Nicolas Jarry at the Chile Open, with the Santiago-born talent electrifying his home crowd with a 1-6 7-6 (7-4) 6-1 semi-final victory over Jaume Munar.
Jarry will get a chance for the second ATP title of his career, and the first since 2019, when he meets Tomas Martin Etcheverry in the final.
Etcheverry emerged victorious 7-5 6-3 in an all-Argentine showdown against third seed Sebastian Baez, earning his first final appearance at this level.
Carreno Busta fell to a 6-3 1-6 7-6 (7-5) second-round defeat against Slovakian Alex Molcan, who progressed to a fourth ATP Tour quarter-final this season.
World number 48 Molcan will next meet Borna Coric after the Croatian eased past Tallon Griekspoor 6-3 6-4, registering back-to-back tour-levels wins for the first time in 17 months.
Second seed Rublev coasted through his first-round clash with Ricardas Berankis, triumphing 6-3 6-4 as he improved his record at the ATP 500 clay-court event in Germany to 10-2.
"I am happy with my performance. Ricardas is a really tough player," said world number eight Rublev, who is aiming for his fourth title of the season after success in Marseille, Dubai and Belgrade.
"He hits the ball really hard and plays fast, so I had to bring intensity from the first game. I am really happy with how I was serving today and I hit some great shots from the baseline.
"The game he broke me in the second set he played really well. He returned really aggressively and I don’t think I made one first serve. But then I kept [my] focus and broke him straight away again."
Alejandro Davidovich Fokina was another comfortable winner, easing past Jozef Kovalik 6-2 6-2 to set up a quarter-final contest with Lorenzo Musetti, who beat Emil Ruusuvuori 6-4 7-5.
Play was suspended early at the Swiss Open due to bad weather, with Spaniard Jaume Munar downing Alexander Ritschard 6-3 6-3 in the only match of the day to reach the last eight.
That meant top seed Casper Ruud will have to wait until Thursday to face Jiri Lehecka in Gstaad, with third favourite Roberto Bautista Agut also seeing his match with Juan Pablo Varillas pushed back a day.
Shapovalov was beaten by fellow Canadian Vasek Pospisil in his opening match at the Oden Sud de France last week after falling at the first hurdle at the Australian Open.
The world number 16 suffered another setback on Monday, going down 6-3 7-6 (7-3) to the unseeded Dimitrov.
Dimitrov was beaten by outsider Gregoire Barrere in his first match in Montpellier last week but claimed a fourth tour-level victory of the year after saving all three break points he faced against the eighth seed.
The former world number three could face another Canadian in the form of Felix Auger-Aliassime or German Jan-Lennard Struff in the second round.
Roberto Bautista Agut, the sixth seed, came from a set down to defeat Marton Fucsovics, while fellow Spaniard Pablo Carreno Busta downed Adrian Mannarino 7-5 6-7 (3-7) 6-4.
Dan Evans advanced in the final match of the opening day of the tournament, seeing off qualifier Philipp Kohlschreiber 6-3 7-5.
Tsitsipas, who took Novak Djokovic to five sets in the French Open semi-finals this month, had come from behind to beat Jan-Lennard Struff in his opener in Austria but was this time on the wrong end of a fightback.
The Greek edged the first set after a tie-break but failed to convert either of his break points in a 6-7 (5-7) 6-4 6-3 reverse.
It was Dimitrov who prevailed after two hours and 14 minutes for his first top-10 win of the season, securing a quarter-final against Dan Evans.
"It's never easy to come out of a situation like that," Dimitrov said. "I was focused, but he went for it.
"In the tie-break a few close calls here and there went his way. [There was] not much else I could have done, I felt. But I kept on believing and kept on doing the right things.
"I stayed in the match, which I think was the most important thing. He's such a great competitor. You always have to be ready. I was just focusing on the most simple things of the game."
The other seeds found life a little easier on Thursday, with Dominic Thiem and Andrey Rublev each through to face one another.
Reigning champion Thiem brushed aside Cristian Garin in straight sets, while Rublev was granted a walkover as Jannik Sinner succumbed to a foot injury early in their meeting.
Daniil Medvedev also advanced but needed three sets after dropping the first to Vasek Pospisil.
Djokovic was not in action, meanwhile, but learned the identity of his Friday quarter-final opponent as Lorenzo Sonego reached the last eight.
The Serbian brushed aside Cristian Garin in his opener and did likewise in Thursday's match with Van De Zandschulp, prevailing in just 71 minutes in the Kazakh capital.
Djokovic has now won six matches in a row and is seeking back-to-back titles after triumphing at the Tel Aviv Open last week – his 89th ATP singles crown.
He reeled off five games in a row in the second set to advance 6-3 6-1, with that his 30th tour-level victory of the year.
And as Djokovic nears the end of a rather mixed season, the 21-time grand slam winner is in the mood to add further titles to his collection.
"My season is different from any other so don't look at my season in comparison to others," he said in his post-match interview.
"I haven't played for over three months before Israel so I definitely am physically and mentally motivated to do well."
Awaiting Djokovic in the quarter-final is Karen Khachanov, who eliminated Marin Cilic with a 2-6 6-3 6-3 comeback victory.
World number four Daniil Medvedev also advanced thanks to a 6-3 6-2 win over Emil Ruusuvuori, while Hubert Hurkacz beat Alexander Bublik 6-4 6-4.
At the Japan Open, third seed Taylor Fritz defeated Hiroki Moriya in three sets and will now face fifth seed Nick Kyrgios, who recovered to beat Kamil Majchrzak 3-6 6-2 6-2.
Denis Shapovalov, looking to build on his run to the Seoul Open final, got the better of home hope Rio Noguchi with a 6-3 6-1 win to advance to the quarter-finals.
World number one Djokovic suffered a shock third-round exit to Dan Evans at the Monte Carlo Masters last week but ruthlessly dispatched Kwon Soon-woo 6-1 6-3 in his home city of Belgrade.
Djokovic broke his opponent five times to set up a meeting with eighth seed and fellow Serbian Miomir Kecmanovic, who battled past qualifier Arthur Rinderknech in three sets, in the quarter-finals.
"I thought it was a pretty flawless performance," Djokovic said. "I moved well, I was mixing up the pace quite well, making him play. I served well in the important moments, [and] overall I just felt great."
On playing in front of his family and friends, the two-time Serbia Open champion added: "It gives you an extra push, an extra motivation, energy to really give your best and leave it all out on the court.
"I think also that made me feel comfortable and confident on the court and I played really good. I'm really pleased with the quality of tennis."
Second seed Matteo Berrettini defeated fellow Italian Marco Cecchinato 6-4 6-3 and will face either Filip Krajinovic or Nikola Milojevic in the last eight of the clay-court tournament.
Over in Barcelona, Nadal – an 11-time champion at the event – was out to make a statement after a rare defeat on the dirt to Andrey Rublev in Monte Carlo.
But the 'King of Clay' needed two hours and 20 minutes to fight back against the unheralded Ivashka 3-6 6-2 6-4 to reach the round of 16, where he will face Kei Nishikori. Nadal is now 62-4 at a tournament where he once won 41 straight matches.
Second seed and Monte Carlo champion Stefanos Tsitsipas hammered Jaume Munar 6-0 6-2, while third seed Rublev - runner-up to the Greek on Sunday - joined Pablo Carreno Busta (6) and Alex De Minaur (14) in making it through.
Evans was unable to follow up his run in Monte Carlo with the 16th seed beaten by Corentin Moutet in a lengthy three-setter, while Fabio Fognini (9) was defaulted for unsportsmanlike conduct after verbally abusing a line official when trailing 6-4 4-4 to Spanish qualifier Bernabe Zapata Miralles.
The world number one will meet Kohlschreiber in the last 16 after he eased to a 6-1 6-2 win over Malek Jaziri on Monday, while the German emerged triumphant from a three-set battle against Mohamed Safwat.
Djokovic fell to a shock 6-4 6-4 defeat to Kohlschreiber in Indian Wells last year on the last occasion the two players met on a hard court.
While he has won three meetings with the 36-year-old since then, twice on clay and in another on grass, Djokovic will be taking no chances.
"I am aware of what he is capable of," Djokovic said.
"I lost to him in straight sets in Indian Wells last year. He actually likes playing top players on a big stage.
"He has lots of experience. He's very fit. He keeps on playing even at that age on a high level.
"I certainly will not underestimate him, I will prepare myself."
Djokovic is playing in Dubai for the first time since 2016, when he retired due to an eye injury in a quarter-final meeting with Feliciano Lopez.
He is a four-time champion and also made the final in 2015, when Roger Federer defeated him.
"As I've said in the press conference prior to the tournament, I miss playing here," said Djokovic, who has a 14-0 record in 2020 following his ATP Cup and Australian Open triumphs.
"I really enjoy it. I enjoy night sessions and I'm feeling good on the court.
"[The Jaziri match] was another testament to the way I feel. I have confidence, I am obviously striking the ball well. Hopefully that can continue in the next match."
The world number one had battled from a set down against Laslo Djere 24 hours earlier and was once more made to work hard for his win versus Miomir Kecmanovic.
The seventh seed took the opener without facing a break point and led early in the second set too.
But Kecmanovic could not hold off Djokovic, who recovered to win 4-6 6-3 6-3 and reach the last four for the fourth time in five campaigns in Belgrade.
After two victories in two nights against Serbians for the two-time winner, Djokovic is on a 10-0 run in matches with his compatriots and 27-4 all-time.
The 20-time grand slam champion also has a 36-6 record in Serbia and has particularly enjoyed the "strange" opportunity to face his countrymen in front of a home crowd.
"It's a very strange feeling, sharing the court with your compatriots," he said. "Obviously the crowd was phenomenal for both players in yesterday's match and today's.
"They're very rare occasions when I'm able to play at home and experience this atmosphere, so I'm trying to enjoy every single moment."
Djokovic is the last Serbian remaining in the tournament, though, and takes on third seed Karen Khachanov – a winner against Thiago Monteiro – in the semis.
There remain two quarter-finals to play on Friday, as Andrey Rublev faces Taro Daniel while Fabio Fognini welcomes the challenge of Oscar Otte.
Meanwhile, there were only two matches completed at the Barcelona Open due to rain, but Ilya Ivashka ensured fans were rewarded for their patience as he took Stefanos Tsitsipas the distance.
Ivashka eventually went down 6-1 4-6 6-2 to the top seed in a heavily delayed second-round contest.
The world number one, competing in the Austrian event for the first time since winning it in 2007, saved a set point in a tie-break during the opener on his way to a 7-6 (8-6) 6-3 triumph.
He had to work hard as Krajinovic, who lost to Djokovic in last month's Italian Open at the last-16 stage, twice broke serve in a tight opener, helping establish a 5-3 lead at one point.
Djokovic hit back in the 10th game to break his opponent for a second time as the opener went to a tie-break, which he edged 8-6 after Krajinovic failed to convert an opportunity when 6-5 up.
The second set was far more straightforward for the 33-year-old, however, as he held serve throughout and broke Krajinovic once to progress through.
"We practiced a few times [together] before coming to Vienna," Djokovic revealed in his on-court interview.
"The draw was tough for us to face each other, but there is always extra pressure and importance to a match when you play someone that you know very well."
Borna Coric is up next for Djokovic after the world number 26 beat Taylor Fritz on the opening day of action.
Elsewhere on Tuesday, Grigor Dimitrov held off fellow top-20 player Karen Khachanov 7-6 (8-6) 6-3 in a competitive match, while Hubert Hurkacz beat Attila Balazs in straight sets.
Dan Evans also advanced to the last 16, where Jurij Rodionov awaits, after Aljaz Bedene withdrew with a thigh complaint when a set down.
World number one Djokovic was 16-0 across all matches in 2020 and in his career against Monfils heading into Friday's meeting.
But the 17-time grand slam winner looked set to see his bid for a fifth Dubai championship end prematurely as Monfils led by a set and a break prior to a dramatic conclusion to the second.
Monfils had collected titles in Montpellier and Rotterdam across his own recent winning streak, yet his Djokovic hoodoo somehow continued.
"It was truly an escape," Djokovic said. "He [Monfils] was clearly a better player for two sets. I was fortunate to work my way back in the second set."
The Frenchman was on top early on and broke in just the third game of the opener, later extending his lead courtesy of the latest in a series of tame Djokovic drop shots.
Djokovic was then spectacularly broken to love in the second, only for Monfils' consistency to wane with the finish line in sight.
The top seed capitalised on the second of his first three break points and set about applying intense pressure to the Monfils serve, but two mammoth holds prompted a remarkable tie-break.
Monfils squandered three opportunities for victory as 10 of the first 11 points went against the serve, Djokovic eventually seizing his fourth set point of the breaker and ninth of the set with a double fault.
Showing visible signs of fatigue, Monfils was broken to love early in the decider and dropped serve again before calling for the trainer, with brief treatment to his left leg unable to arrest the slump as Djokovic clinched a 2-6 7-6 (10-8) 6-1 victory.
Djokovic will next go up against Stefanos Tsitsipas, who cruised through to the Dubai decider for a second year running.
The in-form Greek won the Open 13 Marseille title last week and made it eight straight victories with a comprehensive 6-2 6-3 result against Dan Evans.
Tsitsipas, who lost to Roger Federer in the 2019 final, now believes he can move up another level against Djokovic.
"I'm really impressed by the quality of my game today," he said of the Evans win. "I really hope to bring the same and possibly even better in the next round."
Having won his 89th tour-level title on Sunday in Tel Aviv without dropping a single set, fourth-seed Djokovic wasted no time in securing a win to set up a second-round clash against Botic van de Zandschulp.
Also in Kazakhstan, third seed Stefanos Tsitsipas made hard work of his second-round tie against Luca Nardi, requiring two tie breaks in a two-hour showdown in a 7-6 (7-2) 7-6 (7-3) victory to secure a spot in the last eight.
Andrey Rublev, Roberto Bautista Agut and Adrian Mannarino also sealed their places in the quarter-finals at the Astana Open on Wednesday, while Marin Cilic and Emil Ruusuvuori won their first-round matches.
Meanwhile, Taylor Fritz defeated James Duckworth 6-2 6-7 6-1 in the Japan Open, where there was also a victory for Denis Shapovalov against Steve Johnson.
In the doubles, top seeds Nick Kyrgios and Thanasi Kokkinakis overcame home duo Yoshihito Nishioka and Kaichi Uchida, with second seeds Matthew Ebden and Max Purcell also progressing past the round of 16 stage.
World number one Djokovic only needed a cumulative two hours to see off Malek Jaziri and Philipp Kohlschreiber in his opening matches in the United Arab Emirates and seventh seed Khachanov was unable to provide much more resistance.
The 17-time grand slam champion racked up his 16th win of 2020 in one hour, six minutes to move two matches away from a fifth title in Dubai and ensure he will remain at the top of the rankings come Monday.
After saving a set point, Khachanov became the first player to engineer a break point against Djokovic in the tournament and it was converted when the top seed went long with a forehand.
Djokovic wrapped up the first set when Khachanov buried a backhand into the net and he went a break up in the second after a fine lob.
The world number 17 was unable to return a fierce forehand into the corner when facing match point and consequently exited the competition.
Asked in an on-court interview if he is playing some of the best tennis of his career, Djokovic said: "That's too big of a statement, but I'm definitely feeling well and playing well.
"Tough match for Karen, I think he can do much better than he did. It wasn't his day, but on my side I think I played a very solid match."
Stefanos Tsitsipas came from a set down to defeat Jan-Lennard Struff 4-6 6-4 6-4 and advance to the semi-finals.
The second seed, who won his first title of the year in Marseille last weekend, came from 40-0 down at 4-4 in the decider to break before closing out the victory on serve.
Tsitsipas will face Daniel Evans next after the world number 37 overcame Andrey Rublev 6-2 7-6 (11-9) to reach his first semi-final of the season and fourth of his career.
