The 26-year-old Wimbledon champion had back surgery in September and did not play again until he lost to Jo-Wilfried Tsonga in the quarter-finals of the Mudabala World Tennis Championship exhibition tournament on Thursday.
Wawrinka lost to David Ferrera on the same day and the match between him and Murray was to decide who would finish fifth in the unofficial three-day tournament that sees the world's top two players - Rafael Nadal and Novak Djokovic joining in at the semi-final stage.
Murray looked much sharper against Ferrer than he had looked in the second set against Tsonga and had little difficulty in seeing off the challenge of world number eight Wawrinka.
The world number four got the better of three successive breaks to take the first set and then forged ahead again with a break for 4-3 in the second.
Wawrinka saved a match point on his own serve with a forehand winner, but Murray confidently served out the victory.
In a courtside interview Murray said: "I feel pretty good, a lot better than I did a few months ago. I just need to play more matches like this because the intensity's a lot higher than you can get in practice.
"It was good to get two matches against top players. Everyone needs matches at this stage, especially me. It's been a perfect start and hopefully I'll get better."
Murray will next make the short trip over to Doha where he will play in the AFP season-opener tournament.
In Abu Dhabi the semi-finals being played later in the day see Nadal take on Ferrer and Djokovic going up against Tsonga.