Several quarter-finals were squeezed into Saturday's schedule alongside evening semi-finals following Friday's ranout, forcing Alcaraz to play twice along with Diego Schwartzman who also progressed to Sunday's decider.
Alcaraz first defeated top seed and 2021 Wimbledon finalist Berrettini in three sets, triumphing 6-2 2-6 6-2 in two hours and two minutes.
The 18-year-old Spanish seventh seed, who reached last year's US Open quarter-finals, backed that up with a straight-sets win over Fognini, 6-2 7-5.
"It means a lot to me," Alcaraz said post-match. "I surprised myself to be able to win two matches in a row in the same day. It's tough to win one match, two is even tougher."
Third seed Schwartzman got past fellow Argentine Francisco Cerundolo 7-6 (7-4) 6-3 in a two-hour-and-two-minute semi-final, having won through earlier in the day 7-6 (7-3) 4-6 6-4 against Pablo Andujar.
The top two seeds will meet in the Delray Beach Open final in Florida after wins by Cameron Norrie and Reilly Opelka on Saturday.
First seed Norrie got past American fourth seed Tommy Paul 6-3 6-3 in one hour and 16 minutes. Norrie had endured a slow start to the calendar year, but will now play for a third ATP Tour title.
Second seed Opelka had a tougher outing, needing three hours to overcome John Millman 7-6 (10-8) 6-7 (3-7) 7-6 (7-4). In a match which only saw two breaks of serve,
Opelka, who won last week's Dallas Open title, sent down 16 aces and won 82 per cent of his first serve.
Alcaraz led 6-4 5-3 over the Brazilian wildcard, but was denied a shot at victory as rain interrupted play, which ultimately suspended for the day. Alcaraz's match is scheduled to resume on Wednesday afternoon local time.
The 2022 US Open champion had triumphed last week in Buenos Aires in his first tournament since November following injuries that kept him out of the 2023 Australian Open. Alcaraz is the reigning Rio Open champion.
Cameron Norrie, who Alcaraz beat in the Argentina Open final, progressed with a 7-5 6-1 win over Juan Manuel Cerundolo in one hour and 29 minutes.
Norrie had rallied from a 5-3 deficit in the first set to claim the opening frame, winning 10 of the final 11 games for victory.
Italian veteran Fabio Fognini's charge into the second round was also delayed on the brink of triumph, leading 6-2 5-2 against Chilean qualifier Tomas Barrios Vera when rain intervened.
Fourth seed Francisco Cerundolo won 4-6 6-3 6-3 over Roberto Carbellas Baena while Colombia's Daniel Galan and Peru's Juan Pablo Varillas were also winners on Tuesday.
The 19-year-old phenom has now won all five of his matches in 2023 after winning last week's Argentina Open, and the 2022 Rio champion is now three wins away from defending his title at South America's only ATP 500 event.
Against Fognini, Alcaraz lost the first set despite creating 11 break point opportunities, as his Italian opponent converted all four of his own chances in a back-and-forth battle.
The Spaniard tightened up his service game down the stretch, only allowing Fognini one break point opportunity from the second and third frames combined, and he will now play Dusan Lajovic following his 6-2 6-4 win against Serbian compatriot Laslo Djere.
Chile's Nicolas Jarry is still yet to lose a set in the tournament, following up his impressive upset of third seed Lorenzo Musetti with a 6-2 6-2 triumph over Pedro Martinez.
Jarry will get a crack at another seeded opponent next when he takes on Argentina's sixth seed Sebastian Baez, who emerged victorious 7-5 7-6 (8-6) after two gruelling sets against Peru's Juan Pablo Varillas.
Fourth seed Francisco Cerundolo was eliminated 6-1 4-6 6-1 by Bernabe Zapata Miralles, who will meet Albert Ramos-Vinolas in an all-Spanish quarter-final after he fought off Daniel Elahi Galan 6-2 6-4.
Alcaraz's first-round meeting with Alves was halted on Tuesday due to heavy rain with the 2022 US Open champion leading 6-4 5-3, but the Spaniard clinched victory on Wednesday 6-4 6-4.
The top seed will take on 35-year-old Italian Fognini, who also was made to wait to secure his progress due to the Tuesday rain, eventually triumphing 6-2 6-3 over Chilean qualifier Tomas Barrios Vera.
Second seed Cameron Norrie endured a tough second-round tussle with local Thiago Monteiro, needing two hours and 30 minutes to triumph 7-5 7-5.
The Briton prevailed in one hour and 25 minutes in the first set against the 83rd-ranked Brazilian, while he was broken when serving for the match at 5-4 in the second frame.
Norrie, however, rallied to break straight back before securing victory after successfully serving the match out on the second attempt.
Fifth seed Diego Schwartzman was the major casualty of the day's play, going down 6-1 6-4 to Serbia's Dusan Lajovic in one hour and 29 minutes.
Brazilian veteran Thomaz Bellucci farewelled the ATP Tour after losing 6-3 6-2 to sixth seed Sebastian Baez.
Albert Ramos Vinolas, Bernabe Zapata Miralles and Hugo Dellien were also winners on Wednesday, with the latter progressing into the quarter-finals to face Norrie.
The 18-year-old became the youngest winner of an ATP 500 event since the creation of the category in 2009, clinching a 6-4 6-2 victory in one hour and 26 minutes.
Alcaraz, set to climb into the world's top 20 for the first time, captured his second tour-level title after triumphing at last year's Croatia Open.
The Spaniard won five out of six break points, including a crucial one at 4-4 on his way to taking the opening set.
Third seed Schwartzman – champion in Rio in 2018 – was appearing in his second successive final, having reached the showpiece in Buenos Aires last week.
But the Argentinian was unable to compete with the powerful seventh seed on clay, the surface on which Alcaraz could do major damage in the coming years.
Meanwhile, Cameron Norrie landed his third ATP Tour title after beating Reilly Opelka 7-6 (7-1) 7-6 (7-4) in the Delray Beach Open showpiece.
Top seed Norrie had endured a torrid start to the 2022 season, which began for him with four successive defeats.
Meanwhile, Opelka was seeking a second title in as many weeks following his triumph at the Dallas Open.
The American had won six out of six tie-breaks on his way to victory in Dallas, and a further four this week.
But despite the big-serving second seed hitting 25 aces against Norrie, taking his tournament tally to 81, and 46 winners, a total of 33 unforced errors proved costly.
Although he was denied all five opportunities to break as both sets went to a tie-break, Norrie's service game remained solid throughout and just seven unforced errors underlined his strong performance.
Norrie struggled physically in the Brazilian heat as Navone, playing in his first ATP semi-final, pulled away to win 6-4 6-2.
The pair traded breaks in the opening two games, and then Navone, showing little fear in his first appearance on such a stage, got the break again to go 4-3 up.
Norrie saved break point three times in the next service game, but it was only a temporarily reprieve before Navone took the first set.
The pair traded further breaks at the start of the second set before another slog of a battle in the third game, which saw Norrie save four points on his serve before eventually succumbing.
That proved a turning point as Navone reeled off the next two games to take a commanding lead over a fading Norrie, whose resistance had been broken.
After falling 5-2 down, Norrie received treatment from the physio but got back on his feet to see the game out even though his fate was already sealed.
The two-time grand slam winner hurt his ankle after just two points while playing Brazilian Thiago Monteiro before the Spaniard went on to break his serve.
But just one game later, Alcaraz had his serve broken, shook Monteiro’s hand, and left the court shortly after, retiring from the match.
It comes a week after the 20-year-old lost to Chile’s Nicolas Jarry in the semi-finals of the Argentina Open.
After the match, world number 117 Monteiro said it was “strange” for an injury to occur so early in the match.
“On the court it didn’t look so serious, but then I saw it in the big screen and it was a bad twist,” he said.
“Now I can only cheer for him to recover. He is a star, a dominant one in the new generation.”
Fifth seed Garin – winner of the most recent edition in 2020 – exited a second consecutive tournament at the first-round stage after he was humbled by Federico Coria.
Coria had defeated the fifth seed, Dusan Lajovic, at last week's Argentina Open, too, but was particularly impressive on Tuesday.
A stunning 6-2 6-0 win was sealed in an hour and 16 minutes.
Coria fended off two break points midway through the first set and then won the remaining nine games in succession in a dominant victory.
Garin was the only seed to lose in Brazil, however, as Lorenzo Sonego was on the right side of a 6-2 6-0 scoreline against 2019 winner Laslo Djere.
Fabio Fognini also advanced in straight sets, while Spanish pair Albert Ramos-Vinolas and Fernando Verdasco similarly eased through.
At the Delray Beach Open, 2021 runner-up Sebastian Korda defeated Thanasi Kokkinakis in his first match since winning the Australian Open doubles title with Nick Kyrgios.
Former champion Sam Querrey came up short against Denis Istomin.
The Chilean third seed proved too good for qualifier Mager in the decider, winning 7-6 (7-3) 7-5 after one hour, 34 minutes on the clay in Brazil.
The title win was the fourth of Garin's career and second this month, adding to his Cordoba Open success.
But it was his first at ATP 500 level, having earlier beaten fifth seed Borna Coric in the semi-finals.
Mager, who needed almost three hours to win his semi over Attila Balazs, recovered from a break down in the first set before being edged in a tie-break.
The Italian started the second set well, going a break up and appearing set to force a decider.
But Garin came from 5-3 down, winning 16 of the last 20 points and four straight games to clinch the title.
The third seed advanced with a 6-1 6-1 victory, though that does not quite tell the whole story as the second game of the first set lasted a mammoth 24 minutes and 40 seconds.
Martinez saved eight break points in that lengthy game before finally being outdone by Schwartzman, who will now face another Spaniard in Pablo Andujar.
Incredibly, Martinez won 31 points in the first set but just one game.
"It was unbelievable," Schwartzman said. "This was probably the longest game in the history of the tournament
"I don't remember anything like this before. I played an almost perfect match, I played against an opponent that had as much confidence as me."
Andujar beat Albert Ramos-Vinolas 7-5 5-7 6-3, while fourth seed Pablo Carreno-Busta lost 5-7 6-4 6-3 to Fabio Fognini in the shock of the day.
Federico Coria awaits Fognini after following up his surprise win over defending champion Cristian Garin with a 7-6 (7-2) 4-6 6-4 victory against Fernando Verdasco.
At the Delray Beach Open, top seed Cameron Norrie beat Oscar Otte 6-3 7-5 and will face Sebastian Korda, who saw off Andreas Seppi 7-5 6-3, for a place in the semi-finals.
Tommy Paul and Stefan Kozlov are also through to the final eight in Florida after beating Denis Istomin and Steve Johnson respectively in straight sets.
Down a set when forced off on Friday, top seed Thiem failed to stave off a quarter-final loss once play resumed on Saturday.
Italian qualifier Mager turned his overnight advantage into a 7-6 (7-4) 7-5 victory before again taking to the court later in the day for his semi-final.
The 25-year-old's opponent, lucky loser Attila Balazs, earlier beat Pedro Martinez 2-6 6-4 6-2 but was left clinging onto a place in the tournament when the rain returned, the Hungarian trailing 7-6 (7-4) 3-3 against Mager.
The winner will likely face Cristian Garin in the final after the Chilean third seed opened up a 6-4 4-4 lead over Borna Coric in the other postponed semi-final.
Poor conditions also interrupted the Delray Beach Open, where Milos Raonic was unable to get underway against Reilly Opelka.
The big servers had their semi-final rescheduled for Sunday and will compete for a spot in the decider against Yoshihito Nishioka, who battled from a set down to defeat Ugo Humbert 1-6 6-4 6-0.
Nishioka has reached the final despite dropping the opener in three of his four matches at the ATP 250 event.
"After the first set I just figured out how to play against him and just kept trying to do it and then it worked," he said, as quoted by the ATP Tour.
"If I lose the first set it's okay, I just figure out how he's going to play, how I have to play against him and then from the second set I say, 'Okay, let's do it this way.'"
The highest-ranked Brazilian in the field made a winning start at South America's only ATP 500 event, but he had to work for it, emerging victorious after an 88-minute third set.
A raucous crowd cheered on every point down the stretch, and after saving four break point opportunities to force a tiebreaker, he jumped ahead to a 5-1 advantage and served it out.
He will face the winner between second seed Cameron Norrie and rising Argentine talent Juan Manuel Cerundolo in the next round.
Meanwhile, the top seed in action on Monday – third seed Lorenzo Musetti – continued his recent rough stretch of form with a disappointing 6-4 6-1 defeat at the hands of Chile's Nicolas Jarry.
Musetti, already ranked 18th in the world at 20 years old, has now lost four of his past five matches, while Jarry has won eight out of 10.
Jarry will play Spain's Pedro Martinez in the second round after he spoiled a potential all-Chilean matchup, eliminating Cristian Garin 7-6 (7-0) 6-4.
The only other Brazilian in action, Joao Fonseca, had no luck against Slovakia's Alex Molcan as he went down 6-0 6-3, while Bolivia's Hugo Dellien was similarly dominant in his 6-0 6-2 trouncing of Portugal's Joao Sousa.
After taking a set off world number two Carlos Alcaraz at last week's Argentina Open, Laslo Djere advanced into the second round as Facundo Bagnis retired in the second set while trailing 6-2 3-2.
Norrie eventually overcame the American fifth-seed after a final set tie-break, winning 6-2 1-6 7-6 (7-4).
The Brit's tenacity was key, saving seven of 10 break points, and he will now face another American, Tommy Paul, in the final four in Florida after he beat qualifier Stefan Kozlov 6-3 6-1.
The other semi-final will be contested between Reilly Opelka and John Millman after they bested Adrian Mannarino and Grigor Dimitrov respectively.
Opelka was taken to a third set by his French opponent before winning 7-6 (7-2) 3-6 6-1, hitting 19 aces on his way to victory.
Millan proved too good for third seed Dimitrov winning 6-4 6-4 in an hour and 34 minutes where the Australian's return was a highlight.
At the Rio Open, rain washed out many of the scheduled matches on Friday, with Diego Schwartzman against Pablo Andujar and Miomir Kecmanovic against Francisco Cerundolo both cancelled.
Matteo Berrettini and Thiago Monteiro were finally able to finish their round of 16 match at 11.35pm local time, with the Italian securing victory 6-4 6-7 (6-8) 6-3.
He will play seventh seed Carlos Alcaraz who overcame Federico Delbonis 6-4 7-6 (7-1) after their match was pushed back, starting not long prior to midnight local time.
Defending Rio Open champion Alcaraz was hampered by an injury to his right leg as he was pegged back after taking the opener, with Norrie eventually claiming a 5-7 6-4 7-5 win.
Alcaraz performed admirably despite seeing his movement limited in a nail-biting decider, but Norrie's power ultimately proved too much as the 27-year-old took his fifth ATP career title.
Top seed Alcaraz – playing in his 10th tour-level final at the age of 19 – started well and had forced seven break points by the time he took a thrilling first set, allowing Norrie just one.
With Alcaraz stopping to have his right thigh wrapped after appearing to be in discomfort, Norrie roared back and took the second set following three straight breaks of serve.
That teed up a dramatic finish, with Alcaraz playing a series of delightful drop shots to take the first break of the decider despite playing at walking pace for long periods.
Alcaraz stopped to tear the wrapping off his leg as the pair traded breaks in front of a lively crowd in Brazil, but it proved a bridge too far for the Spaniard as Norrie pinned him back, hitting several excellent returns to claim his first final success against a top-10 ranked opponent.
"It's so special to win this one, especially after losing a couple of finals already this year," Norrie told Amazon Prime Video. "I had to do it the tough way, you know?
"I was looking done there and I just managed to flip a switch and turn it around. It's a good day, especially on a surface I'm not too comfortable with. I had to battle a lot of demons in the last couple of weeks."
The Austrian was one set away from winning his first grand slam title in Melbourne, only for Djokovic to edge a thrilling encounter 6-4 4-6 2-6 6-3 6-4.
After two weeks to recover from what Thiem acknowledged was a tough defeat to take, the world number four is reflecting positively and looking forward to playing again as top seed at the Rio Open.
Thiem starts his campaign against home hope Felipe Meligeni Alves on Tuesday and is the only top-20 player taking part in the ATP 500 event.
"Coming on clay is like coming home," Thiem, a 2017 winner in Rio, said to the ATP Tour. "I like the surface and also really like South America. It's a completely different atmosphere.
"I've had great experiences, won here, won Buenos Aires twice, so it's very easy for me to come back here."
Of his Australian Open exploits, Thiem added: "I feel great about the performance in Melbourne. It was a hell of a two weeks, beating three top-10 guys and then losing to Novak Djokovic 6-4 in the fifth.
"Of course, it was a huge disappointment. But after some time to reflect, it was a great tournament and start to the season. I hope to keep that good form going."
At a period of the season where hard-court tournaments return to the schedule in Indian Wells and Miami next month, Thiem is not worried about his momentum being disrupted.
He said: "For me, it's no problem to play on clay for one or two weeks and then switch back to hard courts."
The Spanish 19-year-old triumphed 6-7 (2-7) 7-5 6-0 to win in two hours and 43 minutes in Saturday's semi-final.
Alcaraz raced away with the match with a third-set bagel in 32 minutes after both of the first two sets lasted more than an hour each.
The 2022 US Open champion produced one of the shots of the season to go 2-0 up in the third set, producing a remarkable running pass down the line.
Alcaraz had undergone treatment on his upper left leg late in the second set at 5-5 but showed off his toughness to reel off eight straight games.
"I'm so proud of myself," Alcaraz said, having only just returned from injury in last week's Argentina Open which he won. "To be in a final again in my second tournament is a really special moment for me... I couldn't ask for a better start of 2023."
The Spaniard will take on second seed Cameron Norrie in the decider, after the Briton won 6-2 3-6 7-6 (7-3) over Bernabe Zapata Miralles in Saturday's other semi-final.
Norrie needed two hours and 32 minutes to get the better of Zapata Miralles, meaning he has won 13 of his past 15 tour-level semi-finals.
Alcaraz and Norrie faced off in last week's Argentina Open final, which the Spaniard won in straight sets.
Rain wreaked havoc in Rio, where only two quarter-final matches were completed at the ATP 500 tournament on Friday.
Thiem's back is against the wall, with the Australian Open runner-up and world number four down 7-6 (7-5) 2-1 against Mager – who is featuring in his first ATP Tour quarter-final.
Lucky loser Attila Balazs and qualifier Pedro Martinez were also playing when the rain returned in Brazil, with the latter leading 6-2 2-2.
Cristian Garin managed to win through to the semi-finals after the third seed claimed his seventh successive victory by rallying past Federico Coria 2-6 6-3 7-5.
Next up for Garin is fifth seed Borna Coric, who defeated Lorenzo Sonego 7-6 (7-5) 6-3 on the Brazilian clay.
At the Delray Beach Open, second seed Milos Raonic and fellow big server Reilly Opelka will meet in the semi-finals.
Raonic beat Steve Johnson 7-6 (8-6) 6-3 and 2019 New York Open champion Opelka took down Kwon Soon-woo 6-3 6-4 at the ATP 250 event.
"It's going to be tough. He gets a lot of free points on his serve and you've got to make him play," Raonic said.
"You can't just make him play though because he goes for it from the centre of the court. You've got to move in, you've got to find a way to be aggressive."
Elsewhere, Yoshihito Nishioka overcame teenager Brandon Nakashima 3-6 7-6 (7-5) 6-4 and sixth seed Ugo Humbert eased past 2018 winner Frances Tiafoe 6-1 6-2.
Competing in his debut ATP Tour tournament, 18-year-old wildcard Nakashima defeated British qualifier Cameron Norrie 7-5 6-2 on Wednesday.
Nakashima, who is coached by 1987 Wimbledon champion and two-time Australian Open runner-up Pat Cash, is the event's youngest quarter-finalist since Kei Nishikori won the tournament as an 18-year-old in 2008.
"I always knew that I had the game to compete with these high-level pros. I just had to have the right opportunities," said Nakashima, who will face Yoshihito Nishioka after the Japanese blitzed Noah Rubin 6-1 6-2.
"I was just hoping to play a good first-round match here, but after winning these two matches, I have a lot of confidence in my game now… Hopefully I can keep it going."
Reilly Opelka – the fourth seed – dismantled Mackenzie McDonald 6-3 6-4 and Kwon Soon-woo prevailed 6-4 3-6 7-6 (7-0) against Ryan Harrison.
At the Rio Open, third seed Garin beat Federico Delbonis 6-4 6-3 en route to the quarters in Brazil.
Garin, who claimed the Cordoba Open title almost a fortnight ago, hit 22 winners to earn a meeting with Federico Coria after the Argentinian's 6-4 4-6 6-4 victory over Carlos Alcaraz.
Elsewhere, lucky loser Attila Balazs rallied past Thiago Monteiro 1-6 6-1 6-4 and Pedro Martinez trumped fellow Spaniard Pablo Andujar 6-1 6-4.
Thiem, playing his first tournament since reaching the Australian Open final, was pushed by Jaume Munar before winning 6-7 (5-7) 6-3 6-4 on the clay in Brazil.
The Austrian top seed, who won the ATP 500 event in 2017, needed two hours, 41 minutes to advance, having also dropped a set in his opener.
Thiem will face Gianluca Mager in the quarter-finals after the Italian qualifier's 6-3 7-6 (7-5) victory over Joao Domingues.
Borna Coric moved into the last eight courtesy of a 6-3 1-6 7-6 (7-5) win against wildcard Thiago Seyboth Wild.
The fifth seed will meet Lorenzo Sonego, who upset second seed Dusan Lajovic 7-6 (7-5) 7-6 (7-5).
At the Delray Beach Open, Raonic – the 2017 runner-up – served 11 aces in a 7-5 6-3 win over Cedrik-Marcel Stebe that sent him into the quarter-finals.
Steve Johnson awaits the Canadian after overcoming 2017 champion Jack Sock 6-4 5-7 6-1.
Frances Tiafoe, the 2018 winner, and Ugo Humbert set up a last-eight meeting with straight-sets victories over Tommy Paul and Miomir Kecmanovic respectively.
Thiem, last in action in an Australian Open final loss to Novak Djokovic, returned with a 6-2 4-6 6-1 victory over wildcard Felipe Meligeni Alves on Tuesday.
The 2017 champion of the ATP 500 event played on clay in Brazil, top seed Thiem grabbed two breaks of serve in the deciding set.
Having started 2020 with four losses in five matches, Borna Coric found a victory by overcoming Juan Ignacio Londero 7-6 (7-5) 7-5.
Dusan Lajovic joined Thiem and Coric as the three seeds to win, but two fell in the opening round.
Casper Ruud, coming off a title win at the Argentina Open, went down to qualifier Gianluca Mager 7-6 (7-4) 7-5.
Guido Pella, the 2016 runner-up, was edged by Thiago Monteiro 5-7 6-4 7-6 (7-3) after just over three hours.
At the Delray Beach Open, Sock claimed his first non-Laver Cup singles win since late 2018.
The American 2017 champion, a wildcard, battled past last year's winner Radu Albot 3-6 6-3 7-6 (7-2), saving a match point in the final set and breaking down in tears following his victory.
Canadian second seed Milos Raonic brushed past lucky loser Denis Istomin 6-2 6-2 and Reilly Opelka served 20 aces in a 6-7 (5-7) 6-4 7-6 (7-4) victory over Ernests Gulbis.
Ugo Humbert, the French sixth seed, battled through, while third seed Taylor Fritz fell to qualifier Cameron Norrie 6-4 6-7 (4-7) 6-4.
