Wimbledon champion Murray, who underwent back surgery in September, saw off Switzerland’s Wawrinka 6-3 6-4 at the Mubadala World Tennis Championship exhibition.
In his first match back, Murray narrowly lost 7-5 6-3 to Frenchman world number 10 Jo-Wilfried Tsonga.
“I feel pretty good, a lot better than I did a few months ago,” the world number three and Wimbledon champion said.
“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 great start and hopefully I’ll get better.”
Murray is playing in Abu Dhabi as he prepares to return to the ATP World Tour at the Australian Open at the beginning of the season.
The 26-year-old is a three-time runner-up in Melbourne having lost out to Roger Federer in 2010 and Novak Djokovic in both 2011 and 2013.