Sinner, 20, failed to convert two match points in the third-set tiebreaker but recovered to win 6-1, 6-4, 6-7 (8), 6-3 on Centre Court against the 19-year-old Alcaraz. In terms of combined age, it was the youngest men's singles matchup in the round of 16 or later at Wimbledon since 1985, when 17-year-old Boris Becker beat Henri Leconte in the quarterfinals.
The 10th-seeded Sinner had three more match points at 5-2 in the fourth, but the No. 5-seeded Alcaraz saved them all before holding serve. Sinner then saved a break point in the next game before finally converting his sixth match point with a forehand winner.
"For me, I didn't expect it because I wasn't playing so well on grass," Sinner said.
Facing an unexpectedly tough opponent and a pending curfew, Djokovic put his game into another gear to beat both to reach his 13th Wimbledon quarterfinal.
When van Rijthoven, ranked 104th, surprisingly won a 50-minute second set, it looked like the match might not finish before Wimbledon's 11 p.m. curfew. But Djokovic sped through the next two sets to wrap up the win, extending his Wimbledon winning streak to 25 matches, with about 20 minutes to spare and ensure he gets a full rest day on Monday.
After the match, Djokovic said in his on-court interview that he had been unaware of the curfew.
"Wow, OK. Wow, I'm lucky. Thank God. I had some previous experiences of playing a match over two days under the roof -- it's never pleasant if you can't finish the match the same day. I'm glad I did and looking forward to the next challenge," he said.
Djokovic later added that his coach told him that he's heard the All-England Club has had conversations about beginning matches at the main courts earlier.
"Since there are some changes this year that we never thought we'll see in Wimbledon, why not move it for half an hour, one hour earlier?" he said. "I think it would be quite helpful to finish matches maybe not using the roof."
The Belgian player won 7-6 (3), 5-7, 5-7, 6-4, 7-5 in a tight contest that lasted 4 hours, 36 minutes. Goffin also reached the quarters in his most recent Wimbledon appearance in 2019, but he missed last year's tournament with an injury.
Tiafoe called for a physio after winning the third set and was given a pill, then quickly went down 5-1 in the fourth as his first-serve percentage dipped. The No. 23-seeded American held two break points at 5-5 in the fifth set, but Goffin saved them both with powerful serves, then converted his first match point in the next game when Tiafoe netted a backhand.
He is the first British man to reach the quarterfinals since Andy Murray in 2017.
Norrie reached a career-high ranking of No. 10 this year, but this is the first time he's been past the third round of a Grand Slam tournament. The 30th-seeded Paul was playing at Wimbledon for the first time and was trying to reach his second Grand Slam quarterfinal.
ESPN's Tom Hamilton and The Associated Press contributed to this report.