The world number two had chances to take a decisive lead in a breathless first set but it tipped Sinner's way when he cracked a blistering return off the Spaniard's second serve to take the all-important tie-break.
Alcaraz -- the Wimbledon champion and tournament favourite in Novak Djokovic's absence -- then fell apart, gifting Sinner three service games in an error-laden second set to give the world number seven a 7-6 (7/4), 6-1 victory.
Sinner and Medvedev will go toe-to-toe for the trophy on Wednesday.
"In the second set, I was out of my mind," said Alcaraz at a post-match news conference.
"I was just complaining a lot, (and) it's really difficult to play your best if you're complaining or mad at yourself," the 20-year-old added.
"(I've been) trying to take my chances. Today, (I didn't)," he said.
Sinner pointed to a key turning point when, serving at 2-1 in the second set, he recovered from 0-40 to open up a healthy lead.
"There are a couple of points (that) can change the momentum completely," the 22-year-old said.
"I managed somehow to win these kinds of moments today, which obviously helped me in the following games to stay very calm mentally and play with a lot of confidence," he said.
Earlier, third-ranked Medvedev hailed a "perfect service match" as he eased into the men's final with a 6-4, 6-3 win over Alexander Zverev.
The match got off to a close-fought start but Medvedev then notched a crucial break of serve and managed to see out the first set.
It was a similar story in the second set, with the Russian breaking for 5-3 and serving out the match with a pair of fierce aces.
"I don't think there was one bad thing I can say about my serve (today)," Medvedev said at a post-match news conference.
"I think the fact that the play was faster -- the faster the court is, the easier you can hit aces... (and) the easier you feel when stepping into the serve," the 27-year-old said.
The top-ranked women's player Aryna Sabalenka said her performances in "key moments" were crucial to surviving a major scare in the second round, after she defeated unseeded Katie Boulter 7-5, 7-6 (7/2) in Beijing.
Sabalenka saved seven break points at 5-5 and then forced the stubborn Briton, ranked 56th in the world, into a rare backhand error to clinch the opening set.
The Belarusian notched another must-win break in the second set to again draw level at 5-5 before triumphing in a tie-break by slamming down an unreturned serve.
She will battle Italy's Jasmine Paolini in the next round for a place in the quarter-finals.
"I think what made the difference was that in the key moments I played a little bit better than her," Sabalenka said at a post-match news conference.
"I think it was all about those last games in each set. She had the opportunity and I'm super glad that I didn't give her those sets easily."
US Open champion Coco Gauff also had to dig deep to get the better of Croatia's Petra Martic in a rollercoaster tie that lasted three hours.
Martic was serving for the match against Gauff but the world number three fought back to take the game and went on to dominate the ensuing tie-break, winning 7-5, 5-7, 7-6 (7/2).
"Today was a mental victory. I was happy I was able to get through it," said Gauff, who will face Russia's Veronika Kudermetova in her next match.
World number two Iga Swiatek shook off a rain delay to glide past France's Varvara Gracheva 6-4, 6-1 and set up a date with fellow Pole Magda Linette.
Fourth-ranked Jessica Pegula bounced back from a set down to beat Russia's Anna Blinkova 6-7 (2/7), 6-2, 6-1.
The China Open is taking place for the first time since 2019 after Beijing ditched its isolationist zero-Covid policy.
© 2023 AFP