Defending champion Wawrinka, looking for a third title here, seized the initiative with a service break in the opening game.
He was stretched in the second set by the left-handed Muller, but wrapped up the tiebreaker from 4-4.
''The weather was a bit tricky with the wind but I played aggressively,'' Wawrinka said.
The top-seeded Swiss will play fourth-seed David Goffin of Beglium for a place in the final.
Goffin got past unseeded Andreas Haider-Maurer of Austria 7-5, 6-2.
''It's going to be an interesting match (against Goffin). He's a fine player and finished the last year strongly,'' Wawrinka said.
Third-seeded Roberto Bautista Agut of Spain, the 2013 runner-up, advanced after a tough 7-6 (7), 6-4 win against Lu Yen-hsun of Taiwan.
''That was a good match, it took almost two hours,'' Bautista Agut said. ''He had a chance to win the first set but I was there all the time, and confident of winning.''
He said he was looking forward to his semifinal against Slovenian qualifier Aljaz Bedene, who ousted fifth-seeded Guillermo Garcia-Lopez of Spain 2-6, 6-3, 6-2.
''We have known each other for a long time, and I'm happy to see him in the semis,'' Bautista Agut said of Bedene.