Djokovic survived a brief stumble during an evening match to defeat Mikhail Youzhny in the last of the quarterfinals.
Wawrinka did not face a break point in his win over Murray, who had captured 11 consecutive matches at the U.S. Open. Murray defeated Djokovic in last year's final.
Djokovic has not won a tournament since April and has held onto his No. 1 ranking despite the sensational season that has been put together by second-seeded Rafael Nadal.
Nadal, who has won nine tournaments in 2013 and has lost only three matches all year, will meet Richard Gasquet in the other semifinal. Gasquet will also be playing in his first Grand Slam semi.
Wawrinka is 2-12 against Djokovic, although he pushed Djokovic to 12-10 in the fifth set at the Australian Open this year.
Murray had won eight of his previous 13 meetings against Wawrinka.
Wawrinka won three-quarters of the points on serve and nearly half (50-of-109 points) off Murray's serve. He had 42 winners against 37 unforced errors while Murray had 15 winners and 30 unforced errors.
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