The top two seeds Casper Ruud and Diego Schwartzman will face off in the Argentina Open final after the latter won two matches on Saturday to progress at his home event.
The Argentine world number 14 had to overcome countryman Francisco Cerundolo 6-3 2-6 5-7 earlier on Saturday after their quarter-final had been interrupted by rain on Friday evening.
The match was tied at 1-1 in the third set when rain intervened, with Schwartzman triumphing when play resumed to earn a semi-final date with third seed Lorenzo Sonego.
Schwartzman would later beat Sonego 7-5 3-6 6-2 in almost three hours on a busy day for the 2020 French Open semi-finalist.
World number eight Ruud progressed with a routine 6-3 6-3 victory over Argentine sixth seed Federico Delbonis.
At the Dallas Open semi-finals, Reilly Opelka and John Isner broke the record for the longest tiebreaker on the ATP Tour since 1990.
Second seed Opelka triumphed over fellow American Isner but it was not easy, winning 7-6 (9-7) 7-6 (24-22).
Opelka sent down 39-21 aces across the match, earning a spot in the final against fourth seed Jenson Brooksby who beat Marcos Giron 6-4 6-7 (4-7) 7-6 (7-5).
Auger-Aliassime gets the better of Ruud as Medvedev hits Masters 1000 milestone
Casper Ruud's hopes of building on his victory at the Barcelona Open were ended as he lost to Felix Auger-Aliassime at the Madrid Open.
Auger-Aliassime will now face top seed Jannik Sinner in the quarter-finals, after claiming a 6-4 7-5 victory over the fifth seed Ruud on Tuesday.
Ruud, runner-up at last year's French Open and a force to be reckoned with on clay, won in Barcelona earlier in April, but came unstuck against the Canadian.
It was not the only shock exit, as Alexander Zverev, the world number five, succumbed in straight sets to Francisco Cerundolo.
Earlier, Daniil Medvedev claimed his place in the quarters, in which he could face Rafael Nadal, by beating Alexander Bublik 7-6 (7-3) 6-4.
Data Debrief: Medvedev's milestone
Five of the six quarter-finals Medvedev has reached on clay have come at either ATP Masters 1000 or grand slam level.
He has now reached at least the quarter-final stage at all nine Masters events, too.
Alcaraz matches Nadal record as reigning champion scrapes into Madrid Open quarters
Jan-Lennard Struff made life difficult for Carlos Alcaraz, but the reigning Madrid Champion eventually made it through.
Alcaraz had won both of his opening games with the minimum of fuss, but he needed three sets to get beyond Struff, who won a second-set tie-break.
However, Alcaraz eventually prevailed in the decider, clinching a 6-3 6-7 (5-7) 7-6 (7-4) victory.
Alcaraz, who is in the hunt for a third straight title in Madrid, will now face seventh-seed Andrey Rublev for a place in the last four.
Data Debrief: Prodigal son matches the master
There have been plenty of comparisons between Alcaraz and his fellow Spaniard Rafael Nadal.
And with his win on Tuesday, Alcaraz matched Nadal's record for the longest winning run at the Madrid Open, at 14 matches, since the tournament began in 2002.
Sinner fights back to reach first Madrid Open quarter-final
Jannik Sinner has booked his place in the Madrid Open quarter-final, going the distance to beat Karen Khachanov 5-7 6-3 6-3 on Tuesday.
The top seed dropped a set for the first time at the tournament as an in-form Khachanov, but he shook off the concerns of a lingering hip injury to make a comeback.
After winning the second set, he then saved both break points he faced in the decider, finishing off a contest that lasted over two hours.
Sinner has reached the quarter-final of the Madrid Open for the first time and will face either Casper Ruud or Felix Auger-Aliassime next.
Data debrief: Sinner overcomes first big test
Not only has the 22-year-old become the only player to reach the quarter-final at all four Master 1000 events in 2024, but he is the first to achieve that feat since Milos Raonic in 2016.
Sinner has also become the first Italian player to make the quarter-finals of all three existing ATP Masters 1000 events on clay, since 2009 when the Madrid Open took the place of the Hamburg Masters.
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