Alcaraz took just under an hour and 40 minutes to overcome his fellow Spaniard and friend 6-3 6-4, getting 67 per cent of his first serves in and winning 77 per cent of those.
Carreno-Busta struggled to keep the US Open champion at bay, facing 12 break points in all, and although he saved nine of them, his defiance was ultimately in vain.
"It is difficult to play against a friend like Pablo," Alcaraz said on-court after his win on Friday. "Every day we go and have dinner, lunch, together. Every week and we train together, so it is difficult to play against him.
"I also support him and want him to win every match. On court, there are no friends. You have to be focused and go for the match and that is what I did."
Alcaraz will face third seed Felix Auger-Aliassime in the final four after the Canadian defeated Alexander Bublik 6-2 6-3.
The other semi-final will see Roberto Bautista Agut play Holger Rune after the Spaniard beat Stan Wawrinka 7-5 7-6 (7-5) and the Danish teenager defeated Arthur Rinderknech 7-6 (7-0) 6-2.
In Austria, top seed at the Vienna Open Daniil Medvedev beat Jannik Sinner 6-4 6-2 to advance to the last four, where he will play Grigor Dimitrov after the Bulgarian overcame Marcos Giron 6-3 4-6 6-4.
The winner of that contest will face either Denis Shapovalov, who beat Dan Evans 6-3 6-3, or Borna Coric after the Croatian came through against Hubert Hurkacz 6-4 6-7 (2-7) 7-6 (7-5).
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.
Serving was the story of the match as the world number two tallied up 14 aces to his unseeded opponent's zero, and only allowed Martinez to see five second serves in the opening set, with Zverev winning all five. Overall, Zverev won 20 of 24 points on serve in the first set.
The second set was more competitive, with Martinez even breaking back after Zverev jumped ahead and looked to coast to victory, but he could not hold off the Russian down the stretch.
Medvedev will play American Jenson Brooksby in his fourth-round matchup after he won a hard-fought 6-3 5-7 6-4 struggle against 15 seed Roberto Bautista Agut.
In a razor-close contest, Brooksby was just slightly better throughout, winning 60 per cent of his service points compared to the Spaniard's 59 per cent, as well as winning 41 per cent of return points compared to Bautista Agut's 40 per cent.
Fresh off his Indian Wells Masters triumph over Rafael Nadal, Taylor Fritz kept his good form going with a 7-6 (7-2) 6-4 win against American compatriot Tommy Paul.
Fritz, who is now up to world number 13, did not have his serve broken all day, winning 81 per cent of his successful first serves (30-37), while also capitalising on the only two break points he saw.
14 seed Carlos Alcaraz only needed two sets to get past 21 seed Marin Cilic 6-4 6-4, creating nine break point opportunities to Cilic's one, which was saved.
In the late session, and in a meeting of rapidly rising prospects, 22-year-old Serbian Miomir Kecmanovic pulled off an upset 7-6 (7-4) 6-3 win over 21-year-old American Sebastian Korda.
Meanwhile, three seed Stefano Tsitsipas was too much for Australian Alex de Minaur, winning 6-4 6-3 after allowing no break point opportunities in the opening set, and saving all three in the second.
Medvedev looked in all sorts of trouble against the Australian, but the world number two and top seed survived at the ATP 1000 tournament on Sunday.
Canadian sensation Felix Auger-Aliassime was sent packing by former champion John Isner in Miami.
MEDVEDEV ADVANCES… SOMEHOW
Australian Open and US Open runner-up Medvedev could barely walk during his gruelling three-set win against Popyrin.
Medvedev let three match points slip away in the second set, having led 5-2, before cramp set in.
In humid conditions, Medvedev was forced to rely on his serve as he limped around the court.
"Winning a Grand Slam final in straight sets doesn't feel the way I felt after the match point today," he said. "A match to remember for sure."
"I felt like my legs were not following me anymore," Medvedev said. "The only thing I was thinking about is not to fall down, because if you fall down, I don't think I would be able to get up. There were a few moments I just wanted to lay down and say, 'OK, it's over.' That's the thing I couldn't accept myself to do."
Awaiting Medvedev is Frances Tiafoe after he outlasted 16th seed Dusan Lajovic 1-6 7-5 6-3.
AUGER-ALIASSIME TOPPLED
A new year, but same result for 11th seed Auger-Aliassime, who was beaten 7-6 (7-5) 7-6 (7-5) by Isner.
Isner defeated Auger-Aliassime en route to the championship match in Miami two years ago and the big-serving American repeated the feat.
The only former Miami champion in this year's field, Isner remains unbeaten in tie-breaks at Hard Rock Stadium, winning all 11 since the tournament relocated in 2019.
"It was a big test for me. There's probably not many places in the world where I like my chances against Felix," Isner said. "I'm kind of lucky to play him here in Miami, where I like it a lot. If I were to play him on clay somewhere in Europe, it'd probably be a different story."
Next up is seventh seed Roberto Bautista-Agut, who beat Jan-Lennard Struff 4-6 6-3 6-2.
Elsewhere, Jannik Sinner, Taylor Fritz, Emil Ruusuvuori and Alexander Bublik also advanced.
Although the 37-year-old Wawrinka is no longer at his best – ranked 322nd in the world – he still put up a strong fight against his 23-year-old opponent, creating eight break point opportunities in the match while facing nine.
Ruusuvuori will play eighth seed Hubert Hurkacz in the second round in a tough matchup, while Slovakia's Alex Molcan will play fourth seed Casper Ruud after defeating American Mackenzie McDonald 7-6 (7-1) 6-4.
Molcan's advantage was in his serve, winning 74 per cent (49-of-66) of his service points compared to 59 per cent (49-of-83) for McDonald.
In a clash between a pair of top-30 talents, Russia's Karen Khachanov got the better of Argentina's Francisco Cerundolo 7-6 (7-4) 5-7 6-3. He will play the winner between 13th seed Marin Cilic and Croatia's Borna Coric next.
Recent runner-up of the Atlanta Open Jenson Brooskby had no issues with Kazakhstan's Alexander Bublik, winning 6-2 6-3, and he will likely play Roberto Bautista-Agut in the second round as the Spaniard leads 7-6 (7-5) 2-1 with a break in the second set when a rain delay ended the day's play.
One of Canada's top hopes, Denis Shapovalov, will have his back up against the wall when his match resumes against Alex de Minaur, losing the first set 7-5, with the rain arriving in the middle of the second-set tiebreaker.
Jack Draper will head back onto the court with a set advantage against Hugo Gaston after winning the opener 6-2, although he will have to save a break point first up.
