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.
Thompson, who is ranked 63rd in the world, got the better of Harris, showing to grit to win in two hours and 30 minutes.
In the final match of the day, play was suspended due to rain and lightning after the first set with American Sam Querrey leading 6-4 against German Peter Gojowczyk.
Former world number 11 Querrey sent down 12 aces in the first set before the weather intervened.
The winner of Querrey and Gojowczyk will take on Thompson.
Steve Johnson defeated Alexei Popyrin 7-6 (7-4) 6-3, while Bjorn Fratangelo beat Italian Andreas Seppi 7-5 7-6 (7-5).
World number 49 Harris eased past Ontario-born Schnur 6-3 6-2 in one hour and 17 minutes in Toronto.
Harris sent down nine aces, winning 78 per cent of points on his first serve, converting four from four break points on return.
Nadal is a five-time champion in Toronto, winning the previous two editions in 2018 and 2019.
Marin Cilic, who won his first title for three years in Stuttgart, beat Albert Ramos-Vinolas 6-2 4-6 6-3 in two hours and 13 minutes.
The 32-year-old will face sixth seed Casper Ruud in the next round.
Fabio Fognini also needed three sets to progress, battling from behind to defeat Jan-Lennard Struff 6-7 (2-7) 6-2 6-4 to set up a meeting with Andrey Rublev.
Ugo Humbert impressed in his straight-sets defeat of Lorenzo Sonego and will next face third seed Stefanos Tsitsipas, while qualifier James Duckworth beat Taylor Fritz to secure a showdown with Citi Open winner Jannik Sinner.
Alexander Bublik defeated Briton Dan Evans in straight sets to earn a second round meeting with top seed Daniil Medvedev, while Australian John Millman will face 11th seed Gael Monfils after beating Ricardas Berankis.
Reilly Opelka came from a set down to win over Australian Nick Kyrgios, while Tommy Paul also fought back to beat Canadian Vasek Pospisil.
After coming from a set down to force a decider against Lloyd Harris in his opening match in Rome, Karatsev held serve when facing match point in a back-and-forth tie-break.
The Russian had already missed a chance to break for the match but did not fail at the second attempt, completing a 3-6 6-3 7-6 (9-7) win to book a date with world number one Djokovic.
Djokovic will be eager to get back on track after suffering a defeat to Carlos Alcaraz in the semi-finals of the Madrid Open.
Filip Krajinovic's reward for a 7-6 (9-7) 7-6 (7-4) victory over Frances Tiafoe is a showdown with Andrey Rublev, while Cristian Garin will take on the in-form Alcaraz following a 6-3 6-2 success over wildcard Francesco Passaro.
Marin Cilic was the other main-draw winner on Sunday, cruising past Matteo Arnaldi 6-1 6-4 in an hour and 20 minutes.
Medvedev must reach the semi-finals in order to retake the top spot in the ATP rankings from Novak Djokovic in April, and he got off to a positive start in Miami, not facing a single break point in his 90-minute win.
"On the days when you serve good, your opponent doesn't have this freedom to return, it helps you," Medvedev said post-match.
"[In the] second set, the scoreline was easier, it was much tougher in the beginning, but when your opponent knows you're probably going to get some aces and it's not going to be easy for him to return, he gets pressure on his serve and many times that is what happens in close matches."
Medvedev will face Pedro Martinez, who defeated Cristian Garin 7-6 (6-2) 6-2.
Reigning Miami champion Hubert Hurkacz got his title defence off to a good start with a 7-6 (7-5) 6-2 victory over Arthur Rinderknech.
Following defeats for Murray and John Isner, the Polish world number 10 is the only former champion left in the draw.
A number of men's seeds were beaten in their second-round matches on Saturday, however, including Canadian duo Felix Auger-Aliassime and Denis Shapovalov.
Miomir Kecmanovic continued his good run of recent form, defeating Auger-Aliassime in straight sets 6-4 6-2, while South African Lloyd Harris beat Shapovalov 6-4 6-3.
For his third consecutive ATP 1000 match, meanwhile, Stefanos Tsitsipas was pushed to three sets by an unseeded American.
After some entertaining hitting, with both looking to finish points early, the Greek third seed claimed four straight breaks of serve to eventually defeat Jack Wolf 6-4 6-7 (5-7) 6-1.
Murray, a five-time champion at Queen's, was beaten 6-3 6-3 by Italian Berrettini as the three-time grand slam champion struggled a day on from being given a Wimbledon wildcard.
The former world number one beat Benoit Paire in his first ATP Tour singles match since March on Tuesday, but the 34-year-old revealed he is still being troubled by a groin injury after his loss to Berrettini and knows he must raise his game.
Murray said: "I actually felt my movement was actually quite good for both of the matches. My tennis today was not very good. That's the thing that I'll need to improve the most.
"Then there is still a slight niggle in the groin, so [I have] to try to get rid of that discomfort between now and Wimbledon. I need to be playing points, basically. I played two sets in preparation for this event.
"I do feel like I genuinely have been hitting the ball well in practice, but then like today when you're under a bit more pressure and stuff and you're having to make very split-second decisions when you're on the court, if the guy is serving 140 miles an hour, like, it's difficult to prepare for that."
Dan Evans made history earlier in the day, getting the better of Adrian Mannarino 6-4 7-6 (9-7).
With Jack Draper and Cameron Norrie having already progressed, Evans' win ensured there will be three Britons in the singles quarter-finals for the first time in the Open Era.
Feliciano Lopez will not retain his title in London after the Spaniard went down 6-2 6-3 to second seed Denis Shapovalov. Spanish veteran Lopez won in 2019, with last year's tournament cancelled due to the pandemic.
There will be no glory on home soil in Halle for German Zverev, who was taken out 7-6 (7-4) 3-6 6-3 by unseeded Frenchman Humbert.
Humbert has now beaten a top-10 player on every surface, with Zverev serving 20 aces but bowing out after his 22-year-old opponent claimed the only break of the final set.
Sebastian Korda battled past Kei Nishikori 2-6 6-3 7-5 in Halle, while Lloyd Harris also moved into the last eight at Lukas Lacko's expense.
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).
Coming off an epic three-hour duel Wednesday in his first match since the French Open final, Nadal fell to Lloyd Harris 6-4 1-6 6-4 on Thursday at the Citi Open.
After a short-lived maiden appearance at the Washington, D.C. tournament, the Spaniard will look ahead to Toronto and Cincinnati as he continues his preparations for the U.S. Open.
Harris, meanwhile, heads to a quarter-final matchup against veteran Kei Nishikori after recording the biggest win of his career.
Facing Nadal for the first time, the 24-year-old South African slammed 16 aces Thursday and saved four of six break points.
The 20-time grand slam winner, who battled a foot injury to outlast Jack Sock in his first match, did not have enough to answer the world number 50 on Thursday.
In addition to the top-seeded Nadal's defeat, second seed Felix Auger-Aliassime also went down Thursday, falling 6-3 6-4 to American wild card Jenson Brooksby.
With their exits, the tournament is now without its top four seeds.
That leaves fifth seed Jannik Sinner as the top player remaining after he defeated Sebastian Korda 7-6 (7-3) 7-6 (7-3).
Nishikori advanced by downing seventh seed Cameron Norrie 3-6 6-3 6-3, while John Millman knocked out eighth seed Reilly Opelka 6-3 7-6 (7-4).
Among unseeded players, Denis Kudla defeated the red-hot Brandon Nakashima 3-6 7-6 (7-3) 6-4, while Steve Johnston eased past Ricardas Berankis 6-2 6-1 and Mackenzie McDonald beat Illya Ivashka 6-4 6-4.
In addition to Harris-Nishikori, Kudla will face McDonald in the other quarter-final in the top half of the draw, while Sinner meets Johnson and Millman takes on Brooksby in the bottom half.
By far the most experienced player remaining in the field after Harris' upset of Rafael Nadal on Thursday, Nishikori prevailed 6-3 7-5 to avenge a loss earlier this year in their only prior meeting.
Nishikori had lost his last six ATP quarter-final matches dating to a trip to the semis in Barcelona in April 2019.
The 31-year-old next faces Mackenzie McDonald, who downed countryman Denis Kudla 6-3 6-2 to reach his second career ATP semi-final. He has never played in a final.
In the other semi-final, fifth seed Jannik Sinner will meet wild card Jenson Brooksby.
Sinner had little trouble with American veteran Steve Johnson in a 6-4 6-2 win as the Italian won 93 per cent of his first-serve points and saved all three break points he faced.
Brooksby maintained the strong return game that as carried him all week in a 6-1 6-2 upset of 11th seed John Millman.
The Australian did not manage an ace against the 20-year-old American, who won 54 per cent of the points on Millman's serve and converted five of seven break points.
At 130 in the world, Brooksby is the lowest-seeded Citi Open semi-finalist since John Isner reached the 2007 final while ranked 416th.
The 20-year-old American, who took a set off Novak Djokovic and rattled the world number one at the US Open, is shaping up as potentially his country's biggest hope for the future in the men's game.
Californian Brooksby crushed Spain's world number 44 Alejandro Davidovich Fokina 7-5 6-0, and second seed Schwartzman awaits after the Argentinian took down another 20-year-old American, Brandon Nakashima, scoring a 6-4 6-2 quarter-final win.
Schwartzman is the man who ended Andy Murray's hopes at the tournament in Antwerp.
Brooksby, who had to win two qualifying matches to reach the main draw, said: "Tomorrow will be a great match. I'm really looking forward to it. I'll get some rest tonight and get ready to battle again tomorrow."
The other semi-final will see Italian top seed Jannik Sinner take on South African seventh seed Lloyd Harris following their respective straight-sets wins over Arthur Rinderknech and Marton Fucsovics.
There will be an all-Russian semi-final at the Kremlin Cup in Moscow, after Aslan Karatsev and Karen Khachanov won through to the final four.
Second seed Karatsev sank the hopes of Frenchman Gilles Simon, breaking serve five times on the way to a 6-4 6-3 win, while third-seeded Khachanov edged out Australian John Millman. A 7-5 7-6 (7-4) grind featured 19 aces by Khachanov, the 2018 Kremlin Cup champion, who saved four set points in the second set.
Marin Cilic thrashed Pedro Martinez 6-1 6-2 to set up a tussle with Ricardas Berankis, the Lithuanian ending Adrian Mannarino's run with a 6-2 7-6 (7-1) success. Frenchman Mannarino had stunned Russian top seed Andrey Rublev in the previous round.
Tommy Paul took down Rublev, beating the fourth seed for the first time in four meetings, while the ninth-seeded Shapovalov fell to Aslan Karatsev.
The news was not all bad for the higher seeds, though, as US Open champion Medvedev picked up his 50th win of the year.
PAUL DOWNS RUBLEV
Playing in the main draw at Indian Wells for the first time, the 24-year-old American Paul outlasted Rublev 6-4 3-6 7-5 for his second win in eight career matches against top-10 players.
Paul was on the offensive throughout the match, firing 41 winners while making 37 unforced errors, while Rublev had 23 of each.
The Russian will lament missed opportunities, as he converted just four of 14 break point chances before watching Paul break him twice in the final set to prevail.
Paul moves on to face 21st seed Cameron Norrie, who beat Roberto Bautista Agut 6-4 5-7 6-3.
MEDVEDEV NOTCHES 50TH WIN
Medvedev had to work a bit to get past 27th seed Filip Krajinovic 6-2 7-6 (7-1), improving to 38-5 on hard courts in 2021. Only Stefanos Tsitsipas (52) has more victories overall this year.
The Russian had 25 winners and 18 unforced errors while winning 70 per cent of points on his first serve.
He next faces 23rd seed Grigor Dimitrov, who downed 16th seed Reilly Opelka 6-3 6-4.
KARATSEV UPSETS SHAPOVALOV
Playing at Indian Wells for the first time, 19th seed Karatsev upset Shapovalov 7-5 6-2, saving the only break point he faced in the match.
Casper Ruud, seeded sixth, rallied past Lloyd Harris 6-7 (4-7) 6-4 6-4 as he seeks his sixth tournament title this year.
He will face 11th seed Diego Schwartzmann, who beat 18th seed Daniel Evans 5-7 6-4 6-0 to reach the fourth round at Indian Wells for the first time.
Eighth seed Hubert Hurkacz had little trouble with Frances Tiafoe, rolling past the American in straight sets.
Jannik Sinner, the 10th seed, advanced via walkover when John Isner withdrew from the tournament to fly home and be with his wife Madison with their third child expected to arrive ahead of schedule on Tuesday.
Alcaraz, featuring in an ATP Masters 1000 event for just the second time, was in impressive form as he saw off France's Adrian Mannarino 6-4 6-0.
The teenager, who will face Nadal on his 18th birthday on Wednesday, fired 19 winners as he took the initiative against his more experienced opponent and his reward is significant.
He became the tournament's youngest ever match winner, beating the record set by Nadal.
"For me, [to] play against Rafa is a dream come true," Alcaraz said as he readies himself to go up against the 20-time grand slam winner.
"Since I was a kid, I wished to play a match against Rafa and now I will be able to here [on] the Centre Court of La Caja Magica in Madrid. It is a really special match against Rafa."
He told Tennis Channel: "It's the best present for my birthday."
The biggest casualty of the day was 13th seed Grigor Dimitrov, who lost 3-6 6-3 7-6 (7-5) to Lloyd Harris early on, the South African now 4-0 against top-20 opponents this year.
Two qualifiers in Pablo Andujar and Marcos Giron played out a remarkable encounter that lasted three hours and 21 minutes.
The first set alone clocked in at just over an hour and a half, but eventually Giron came through the gruelling clash 6-7 (8-10) 7-6 (7-4) 7-5 to set up a meeting with third seed Dominic Thiem.
Fabio Fognini defeated Carlos Taberner 7-6 (7-4) 2-6 6-3 for the right to face eighth seed and Italian countryman Matteo Berrettini.
Diego Schwartzman, the seventh seed, awaits Aslan Karatsev after he beat Ugo Humbert in straight sets in what was the Russian's debut appearance at the tournament.
Dan Evans and John Isner were among the other players to secure progress on Monday.
Zverev survived a first-set scare to power past Lloyd Harris 7-6 (8-6) 6-3 6-4 in Wednesday's US Open quarter-final.
The German fourth seed will face either Djokovic, who is bidding to become just the third man to complete a calendar Grand Slam and first since 1969, or Matteo Berrettini for a spot in the men's final at Flushing Meadows.
Zverev – last year's US Open runner-up – said he has been fuelled by his semi-final win over Djokovic at the Tokyo Games.
"It's the biggest tournament in the world, Tokyo. It's the Olympics," Zverev said during his post-match news conference.
"Winning there against the world number one, especially that I was down a set and a break, being kind of out of the match, then coming back, it was different than the other matches. The emotions were different.
"Also securing a medal for Germany was very special to me. This year it seems like nobody can beat him in a big match, nobody can beat him at the grand slams.
"I feel like I was the first player to beat him in a very big match this year. That does give you something. To any person it would give you something.
"As I said before also, I think it was very important for me to back it up in the finals, back it up in Cincinnati. Hopefully I can continue this streak."
Zverev is in the midst of a career-best 16-match winning streak and has clinched 37 of 40 sets on the hard courts after winning Olympic gold and his fifth career ATP Masters 1000 crown in Cincinnati.
The 24-year-old is bidding to become the second man in history to win Olympic gold medal and the US Open/US Championships title in the same season, after Andy Murray in 2012.
On preparing against Djokovic, Zverev added: "You have to be perfect, otherwise you will not win.
"Most of the time you can't be perfect. That's why most of the time people lose to him. Against him, you have to win the match yourself. You have to be the one that is dominating the points. You have to do it with very little unforced errors.
"He is the best player in the world. He is very difficult to beat. But he's still also got to win tonight. He's playing Matteo Berrettini who is in very good form, finals of Wimbledon. I think he's looking forward to that match, as well. It's going to be an interesting match to watch those two."
