A strange match full of momentum shifts and lulls was absorbing rather than gripping but Medvedev did not care as he triumphed 6-7(7), 6-4, 7-6(4), 2-6, 6-3 on a covered Centre Court.
It snapped Medvedev's five-match losing sequence to Sinner and avenged his bitter defeat by the Italian in this year's Australian Open final when he squandered a two-set lead.
Medvedev, who is bidding to add to his 2021 US Open title, will face defending champion Carlos Alcaraz in his ninth Grand Slam semi-final.
"I knew if I wanted to beat Jannik it needs to be a tough match. He's not any more a guy you can beat easy," the engaging Medvedev said on court.
"It's actually very tough. One moment I could feel that he doesn't move that well so it's always tricky because you want to play more points to make him suffer a little bit more. In a good way.
"But you know at one point he was like 'OK I can't run anymore and I'll go full power' and that's what he did."
Top seed Sinner, who fell at the semi-final stage last year to Novak Djokovic, won the opening set in a tight tiebreak after saving a set point.
But mistakes began to creep into his game, and after losing the second set courtesy of a sloppy service game he required medical attention early after dropping serve at 1-1 in the third and disappeared off-court, apparently feeling ill.
"Already this morning I didn't feel great. Had some problems. Then with the fatigue, it was tough," said Sinner.
"But take nothing away from Daniil. I think he played very smart. He played good tennis. That's it."
"It was not an easy moment. I tried to fight with that what I had today."
GROGGY SINNER
Sinner looked groggy on his return to Centre Court but suddenly snapped back to life and recovered from 5-3 down in the third set with some aggressive hitting as Medvedev's game went off the boil.
But he could not convert two set points in the 12th game and was dragged into a tiebreak that Medvedev sealed with an ace.
Sinner dominated the fourth set, dropping only 12 points, and looked the favourite heading into the decider as for the 36th time at this year's Wimbledon a men's singles went the distance - a new record for a Grand Slam tournament in the professional era.
Russian Medvedev refocused though and got an early break of serve which ultimately proved decisive as he calmly ticked off the games for victory in exactly four hours.
Having snapped his losing run against Sinner, Medvedev is now looking ahead to trying to overturn his straight sets defeat by Alcaraz at Wimbledon last year.
Asked what he needs to do to, he told reporters: "Just play better. I have to serve better. That's still the most important thing on grass.
"You serve aces, you serve on the line, you're less in trouble, and you feel better."
