The Russian is the first man from his country to reach the semifinals in New York since Mikhail Youzhny in 2006 as he defeated Wawrinka for the second time in as many meetings.
Medvedev battles injury, Wawrinka to reach last four
Medvedev was off the mark early, breaking Wawrinka after the Swiss overhit a backhand following a series of stretch volleys. The Russian overcame early nerves on his own serve, saving a break point in the third game and double faults in the next.
The fifth seed continued to give Wawrinka chances to break, but he was unable to convert, Medvedev holding for 4-2, although not with much conviction. The trainer was called by Medvedev and treated his thigh on the next two changeovers.
Serving for the set at 5-4, the Russian was broken to love after having the strapping on his left thigh taken off. The set would go to a tiebreaker in which the fifth seed got out to a 3-0 lead and extend it to 5-2 after a delectable drop shot/lob combination.
Wawrinka would win the next four points, the last on a sizzling backhand return before Medvedev took the final three, the last on a backhand miss by the Swiss, to claim the opening set. Despite the thigh injury, Medvedev broke in the fourth game of the second set after an unforced error by the 23rd seed.
In control now, Medvedev surrendered Wawrinka's service games to concentrate on his own, which proved to be an effective strategy as he blazed through the remainder of the set to go up two sets to none.
The Swiss took immediate control of the third set with a love hold and a break, aided by two Medvedev double faults and a long rally won by Wawrinka for a 2-0 lead. The next four games went by in a flash as each man held twice.
The Russian had a half-chance at 15-30, but Wawrinka held, helped by an ace and a feathery drop shot. Serving for the set, the 23rd had to fend off four break points, finally closing out the set when Medvedev netted a forehand to cut the deficit to two sets to one.
The Russian was quick off the mark in the fourth set, holding to love and breaking when Wawrinka couldn't return his cheeky lob. After surviving some tense moments on his own serve, Medvedev secured the double break after Wawrinka missed a backhand.
Serving for the match, the Russian held to 15, finishing off the victory with an inch perfect backhand lob for his 20th win in his last 22 matches and a spot opposite Grigor Dimitrov in the semifinals.