The Spaniard erased any doubts about his form with a razor-sharp display in his final Red Group match to join Medvedev in the semi-finals of the year-ender.
Third seed Medvedev, who had already qualified, also produced some stunning tennis but Alcaraz pounced to snatch decisive service breaks in each set.
Despite his opening match loss to Germany's Alexander Zverev (26), Alcaraz tops the Red Group and will face Green Group runner-up Novak Djokovic (36) in a mouth-watering semi-final.
The other semi-final will feature Medvedev against home favourite Jannik Sinner (21).
Group play will conclude later on Friday with Zverev up against Andrey Rublev (26) with only prize money at stake.
Medvedev looked the more dangerous player in the early exchanges and failed to convert break points in the fourth game.
But Alcaraz, who is making his debut at the tournament, found another gear at 3-3 as he played four stupendous points to break to love.
He then pounced again at 4-4 in the second set as some errors by Medvedev helped him secure the break of serve. He then completed victory in emphatic fashion.
"I had to stay strong mentally, I was struggling a little bit on serve and his return game is amazing," Alcaraz said on court. "I stayed calm and strong."
Alcaraz and world number one Djokovic will meet for the first time since he lost to the Serb in the Cincinnati final.
