World number one Alcaraz beat Tommy Paul (25) 6-4, 6-4 in the fourth round, while Rybakina notched up her 12th straight win with a 6-3, 6-0 thrashing of Martina Trevisan (29) to reach the semi-finals.
Alcaraz showcased his sensational speed and reflexes to reach a drop shot for love-30 and broke Paul two points later for a 3-2 advantage.
An acrobatic overhead winner gave Paul a breakpoint at 5-4 but Alcaraz recovered, unleashing a perfectly disguised drop shot of his own that Paul could not chase down to claim the first set.
Paul fell behind an early break again in the second set on a missed forehand for 2-1.
The American, who came from behind to beat Alcaraz in their only previous meeting at last year's Rogers Cup, then fended off a match point while serving at 5-3.
But there would be no escape from Alcaraz, the top-seeded teenager letting out a mighty roar when Paul's forehand landed out to end the contest.
"The key of that match was that I was playing to attack," Alcaraz said. "I didn't let him play his game - attack and go to the net - I did those things first... I played a really complete match."
Alcaraz is now three wins away from securing the 'Sunshine Double' after his victory at Indian Wells last week - a triumph that would see him retain the world number-one ranking ahead of Novak Djokovic.
In the quarter-finals, the Spaniard will play another American in Taylor Fritz (25), who eased past Denmark's Holger Rune (19) 6-3, 6-4 earlier in the day.
Daniil Medvedev (27) swept aside Quentyn Halys (26) 6-4, 6-2 in just over an hour in a contest that started after midnight, sealing his place in the quarter-finals for the third successive year when the Frenchman netted a backhand.
"I thought it was going to be cancelled," Medvedev said. "Really happy that I was able to play not so bad ... I'm usually asleep at midnight."
At the Grandstand, Italian 10th seed Jannik Sinner (21) breezed past sixth seed Andrey Rublev (25), firing off more than two dozen winners to win 6-2, 6-4.
SEVENTH TIME A CHARM
Khachanov, seeded 14th, earned his first win over Tsitsipas in seven meetings, taking down the Greek world number three 7-6(4), 6-4 in the fourth round to end a 23-match winless run against a top-10 opponent.
Tsitsipas, who got a first-round bye and second-round walkover, beat Cristian Garin (26) in his Miami Opener on Monday but never found his best level against Khachanov, who controlled the match by winning almost 90% of his first-serve points.
Khachanov will face Argentina's Francisco Cerundolo (24) in the quarter-finals after he beat Lorenzo Sonego (27) 3-6, 6-3, 6-2.
"They say third time is a charm, but for me it took seven times, so I'm super happy," said Khachanov, who lost to Tsitsipas in the semi-finals of this year's Australian Open.
"Not most importantly that I beat Stefanos, but I think with the way I'm playing... I'm just happy to continue that level."
RYBAKINA ROLLS ON
Wimbledon champion Rybakina has been in rare form this year after reaching the final of the Australian Open and was hardly troubled as she extended her winning streak.
The 10th seed deployed her clean groundstrokes and feasted on Italian 25th seed Trevisan's soft second serve in the tight first set.
But it was all Rybakina in the second, the powerful and precise Kazakh pounding an unreturnable serve on match point to set up a last-four meeting with Jessica Pegula (29) who beat Anastasia Potapova (21) in a late-night thriller 4-6, 6-3, 7-6.
"Maybe I'm moving not as good as I was moving in Indian Wells but overall I think that I'm trying to keep that level from Indian Wells," she said.
"There are a lot of ups and downs, but I think overall it's not bad."
World number three Pegula saved two match points late in the third set before dominating in the tiebreaker. The match was hit with a nearly four-hour rain delay before Pegula sealed her spot in the semi-finals for the second straight year.
