Sinner edged a tight first set in the latest chapter of his growing rivalry with world number two Alcaraz before the Italian went on the offensive in the next to reel off the games and seal his fourth win over the Spaniard in seven meetings.
"I'd say every match against him is very tough," Sinner said.
"We both show great respect and play great. Today I played a little better in the important moments.
"The second set was 6-1 but he had a lot of chances. I tried to stay focused. The first set was more of a rollercoaster and I had to stay there mentally.
"I'm very happy about the performance."
Earlier, second seed Medvedev had an easier-than-expected 6-4, 6-3 semi-final win over familiar rival Alexander Zverev.
This was the fifth meeting between the pair this year and although Russian world number three Medvedev won three of the previous four, Zverev had won their most recent clash in Cincinnati.
Zverev won the Chengdu title last week, but the German's seven-match winning streak ended as Medvedev's strong serve saw him save all four breakpoints he faced.
"I'm really happy with my level. Roof closed, different conditions today, much faster," Medvedev said.
"Both of us are big servers so it came down to a few opportunities and I managed to serve better when I had breakpoints to save than he did."
In the women's tournament, top seed Aryna Sabalenka rallied from behind in both sets to beat British qualifier Katie Boulter 7-5, 7-6(2) and set up a third-round clash with Jasmine Paolini.
Sabalenka said she hoped to avenge her 2022 Indian Wells defeat by the Italian.
"Last year at Indian Wells, I wasn't in my best shape. I was struggling with a lot of different things," Sabalenka said.
"I'd say it wasn't me last year. I'm happy to have this opportunity for revenge."
US Open champion Coco Gauff sealed her 14th straight win as the 19-year-old overcame Croatia's Petra Martic 7-5, 5-7, 7-6(2) to reach the round of 16, where she will play Tokyo winner Veronika Kudermetova.
Gauff was down for the count with Martic serving at 5-4 in the decider, but the third seed broke to go level and raised her game in the tiebreak to deny her opponent a fifth career top-five victory.
The American's frequent doubles partner Jessica Pegula also had to dig deep for a 6-7(2), 6-2, 6-1 win over Anna Blinkova.
Pegula was playing her first match at the tournament having received a bye following her run to last week's Tokyo final. The 29-year-old faces 2017 French Open champion Jelena Ostapenko seeking a fourth win in their fifth meeting.
World number two Iga Swiatek progressed with a 6-4, 6-1 win over Varvara Gracheva and fifth seed Elena Rybakina beat Tatjana Maria 7-5, 6-0 after Ons Jabeur lost 7-6(5), 6-1 to Marta Kostyuk.
