Alcaraz, the world number two who can regain the top ranking with a win this week, had a short night's work on Stadium Court as Britain's Jack Draper retired with an abdominal injury with the Spaniard up 6-2, 2-0.
World number one Swiatek, meanwhile, had the last word in most of the long rallies as she powered past 2021 US Open champion Emma Raducanu 6-3, 6-1.
Their smooth progression was a stark contrast to the drama earlier in the day, when Medvedev shook off a second-set fall and badly twisted ankle to beat Zverev 6-7 (5/7), 7-6 (7/5), 7-5 to push his ATP win streak to 17 matches.
The world number six, coming off ATP wins in Rotterdam, Doha and Dubai, rolled his right ankle and lay on the court for several minutes before limping to his chair.
Zverev, who suffered three torn ankle ligaments at last year's French Open, looked on in concern, but after the injury was examined and taped by medical staff Medvedev continued -- and turned the match around.
"In the beginning it was quite painful, so I was more concerned and focused on my ankle than the game," Medvedev said.
"Then that actually helped me a little bit to play better. For the rest of the match, adrenaline was probably kicking in. So it was not easy to walk, that's why I was limping, but to move was easier."
He saved all 10 break points he faced in the second set, grabbing a 4-1 lead on the way to victory in the tiebreaker.
Up an early break in the third, Medvedev wasted a match point as he was broken in the 10th game.
Zverev couldn't build on that, however, and Medvedev held at love to clinch the win after three hours and 17 minutes.
Ankle allowing, Medvedev was scheduled to face 28th-ranked Spaniard Alejandro Davidovich Fokina -- a 6-3, 6-4 winner over Chilean qualifier Cristian Garin -- on Wednesday.
Alcaraz will have a day off before facing Felix Auger-Aliassime, who saved six match points -- three in the third-set tiebreaker -- in his 3-6, 6-3, 7-6 (8/6) victory over Tommy Paul.
Not that Alcaraz will need the rest after his 46-minute outing.
"This is not the way anybody wants to win a match," Alcaraz said.
Swiatek's match followed a familiar pattern, with last year's French and US Open winner feeling out her opponent over a few close games before pulling away for a convincing win.
"I just feel like in these longer rallies I was the one who showed I can bring the pressure on defense and it's not easy to finish the rally.
"She was actually doing the same," Swiatek said. "She was running to every ball and she played those slices which are tricky, but honestly I'm pretty happy with how positive I was and disciplined."
She next faces Romania's Sorana Cirstea, who battled to a 6-4, 4-6, 7-5 victory over fifth-ranked Caroline Garcia of France.
- Kvitova escape -
Men's defending champion Taylor Fritz defeated Hungarian Marton Fucsovics 6-4, 6-3 in a tense match that belied the straightforward scoreline.
Fritz will face Italian Jannik Sinner, who beat three-time Grand Slam winner Stan Wawrinka 6-1, 6-4.
Britain's 2021 champion Cameron Norrie beat seventh-ranked Andrey Rublev 6-2, 6-4 to line up a clash with American Frances Tiafoe, a 6-4, 6-4 winner over Chilean qualifier Alejandro Tabilo.
Australian Open champion Aryna Sabalenka reached the quarter-finals for the first time with a 6-3, 2-6, 6-4 victory over Barbora Krejcikova.
Sabalenka next faces 19-year-old American Coco Gauff, who squeezed past Swedish qualifier Rebecca Peterson 6-3, 1-6, 6-4. Gauff, the fourth seed, has won three of their prior four meetings.
Two-time Wimbledon champion Petra Kvitova, a former world number two now ranked 15th, saved four match points in a 6-2, 3-6, 7-6 (13/11) victory over third-ranked Jessica Pegula.
The Czech next faces last year's runner-up Maria Sakkari, the seventh seed who beat Karolina Pliskova 6-4, 5-7, 6-3.
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