Sinner, looking to capture his second major of the season after the Australian Open, won 6-2, 1-6, 6-1, 6-4 and will take on Britain's 25th-ranked Jack Draper for a place in the final.
Sinner, 23, is the only top-10 player to make the semi-finals with number 12 Taylor Fritz due to face US compatriot Frances Tiafoe, ranked 20, in Friday's other last-four duel.
Italy's Sinner had defeated Medvedev from two sets down to claim the Australian Open title before the Russian gained revenge in another five-setter at Wimbledon.
"It was very tough, I knew it would be very physical," said Sinner.
"It was strange in the first two sets, whoever got the break started to roll."
Sinner said he was looking forward to facing Draper.
"We are good friends off the court. He's having an incredible tournament and hasn't dropped a set."
Sinner swept through the opening set on Wednesday with a couple of breaks as the Russian committed 15 unforced errors to the Italian's meagre six.
However, fifth-ranked Medvedev flipped the script with a double break of his own to level the quarter-final.
In a to-and-fro battle, Sinner returned the favour by racing through the third set in just 30 minutes.
Medvedev patiently carved out two break points in the sixth game of the fourth set, both of which were saved.
That allowed Sinner to grab the initiative with the crucial break for 4-3 before going on to seal the victory.
Medvedev had to save 10 of 15 break points in the tie while his dream of making a 10th Slam semi-final was undermined by 57 unforced errors.
