The top-seeded Murray, the U.S. Open and Olympic champion, will play sixth-seeded Milos Raonic of Canada in the semifinals Saturday. Raonic outlasted third-seeded Janko Tipsarevic 6-7 (5), 6-2, 7-6 (7) in a match that took nearly 2 hours, 45 minutes.
In the other quarterfinals, eighth-seeded Kei Nishikori of Japan beat second-seeded Tomas Berdych of the Czech Republic 7-5, 6-4, and Marcos Baghdatis of Cyprus topped Dmitry Tursunov of Russia 6-2, 6-4.
Murray broke Wawrinka in the opening game of the match, but had to battle to hold serve in the next game, staving off three break points before finally going up 2-0.
Murray, who beat Wawrinka in the first round on the way to winning the gold medal at the London Games, came to the net successfully several times in the first set and broke again with an overhead smash after a lengthy rally to take a 4-1 lead. He closed out the set with an ace.
Wawrinka, ranked 16th, broke Murray in the fourth game of the second set to move ahead 3-1 and then held serve to take the set. Playing primarily from the baseline, Wawrinka blasted several winners to level the match.
In the deciding set, Murray broke in the fourth game to take a 3-1 lead, after Wawrinka staved off three break points. Murray's deep returns and some timely passing shots proved decisive in the final set as he closed out the match with another break.
Raonic closed his hard-fought victory with his 24th ace of the match. It was just the second time he played Tipsarevic, with the first being a similarly closely contested match in Chennai earlier this year.