Rain returned to the All England Club, meaning play on Centre Court started under the roof.
Top seed Alcaraz is seen as the biggest threat to Novak Djokovic, who is gunning for a record-equalling eighth men's title and 24th Grand Slam crown overall.
But the Spaniard, who won the grass-court Queen's tournament last month, was made to work hard for the win by his Chilean opponent, seeded 25th, before prevailing 6-3, 6-7 (6/8), 6-3, 7-5.
Alcaraz bounced back from losing his first set of the tournament to lead 2-1 but narrowly avoided going a double break down in the fourth set before rediscovering his mojo.
"I'm really happy with the level that I played to get through this really tough match," said a relieved Alcaraz.
He added: "It was really, really close. He has great shots... I would say the key is to believe all the time and stay focused."
Alcaraz, attempting to become the third-youngest player in the Open Era to win the title after Boris Becker and Bjorn Borg, was playing his second match in two days after rain delays earlier in the week.
Djokovic, by contrast, moved serenely into the last 16 late on Friday, beating Stan Wawrinka in straight sets.
Men's third seed Daniil Medvedev lost the first set against close friend Marton Fucsovics but recovered to win 4-6, 6-3, 6-4, 6-4.
Greek fifth seed Stefanos Tsitsipas, who beat Andy Murray in a five-set thriller over two days in the second round, eased past Serbia's Laslo Djere in straight sets.
Last year's surprise women's champion, Rybakina, who has not hit top form so far, takes on British wild card Boulter, who will receive vociferous backing from the home crowd.
- 'Nothing to lose' -
"I think it's a super great opportunity for me," said Boulter, the only British player left in the tournament.
"I've got nothing to lose. She's clearly the defending champion for a reason.
"I'm going to have a swing and go for it. I've got a lot of tennis behind me. It's time for me to test my skills against an incredible champion."
Also in the women's draw, two-time Wimbledon champion Petra Kvitova stayed on track for a third title by beating Serbian qualifier Natalija Stevanovic 6-3, 7-5.
The Czech former world number two has pedigree on grass but has only made it past the third round once since she claimed her second title at the All England Club in 2014.
"I love playing on grass, for sure," said the ninth seed. "When my serve is working I love it even more.
"I don't think it was the case today but somehow I found a way, which I'm very happy with."
Australian Open champion and second seed Aryna Sabalenka beat Russia's Anna Blinkova 6-2, 6-3.
On the men's side, former Wimbledon finalist Matteo Berrettini goes head to head with big-serving 19th seed Alexander Zverev in a mouthwatering contest.
Berrettini, who lost to Djokovic in the 2021 final, missed the tournament last year after testing positive for coronavirus.
Zverev has been ranked as high as number two in the world and is also a Grand Slam finalist, but missed a huge chunk of last season after tearing ankle ligaments.
Frances Tiafoe takes on Grigor Dimitrov, who is hoping to roll back the years.
Tenth seed Tiafoe is banking on winning the fans over against the experienced Bulgarian, who reached the semi-finals way back in 2014.
"As soon as I smile, the crowd erupts," he said. "It's crazy, but it's cool. I mean, I guess it's a blessing, and hopefully they like me for the next 10-plus years while I keep playing."
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