Murray was tested by Wawrinka but managed to end victorious with a 4-6 6-3 3-6 record.
The Scot got off to a bright start in the opening set by breaking his opponent's serve in the first game. Despite being two games to love, Murray was tested by the Swiss pro but the 24-year-old managed to see the set through and take the lead.
The 26-year-old held his own against the British player and forced a break of serve, which led to the world number 19 drawing level with a double set point.
Murray went on to frustrate his Swiss opponent by cruising through the first five games of the final set but slipped as Wawrinka fought back.
Despite an encouraging comeback from the Swiss number two, the Scot maintained his form and claimed victory with six games to three.
The Japan Open champion will play either Gilles Simon or Matthew Ebden in the quarter-final stage of the competition.