Swiss ninth seed Wawrinka stunned the Olympic and Wimbledon champion 6-4, 6-3, 6-2, to book a last-four date with Djokovic, the 2011 winner from Serbia who ousted Russian 21st seed Mikhail Youzhny 6-3, 6-2, 3-6, 6-0.
"I feel great. I'm really happy. It's amazing for me to be in my first semi-final in a Slam," Wawrinka said. "To beat him in three sets the way I was playing is good."
"He played great. That was the hardest part about the match," Murray said.
"He just hit the ball extremely well. I didn't create a break point chance. He served well. He hit a lot of lines and was going for big shots."
Reaching his seventh US Open semi-final in a row in hopes of a fourth trip in a row to the final, Djokovic lost his first set of the fortnight but reached his 14th consecutive Grand Slam semi-final, the second-longest all-time streak.
Spanish second seed Rafael Nadal, a 12-time Grand Slam champion, and French eighth seed Richard Gasquet, whose only prior last-four Slam run came in 2007 at Wimbledon, will meet in Saturday's other semi-final.
