Murray needed to take just one set to ensure he made the last four and he won the opener 6-4.
The Wimbledon champion, who had already won his first two matches in this week's event, will top the group and secure a semi-final against Milos Raonic on Saturday if he defeats Wawrinka.
Murray is aiming to win the event to ensure he holds off Novak Djokovic in the race to finish the year on top of the world rankings.