World No. 3 Murray defeated Michael Llodra of France in straight sets 6-2, 6-4, 6-3.
"It was more kind of going back onto that court again and I had had much time to enjoy last year because I was so relieved and to acctually be out there and play night match in front of a big crowd was really nice. I performed well. It was good," Murray said.
The Wimbledon champion will next face Leonardo Mayer of Argentina on Friday.
Meanwhile in the women's singles, former US Open champion Venus Williams went down to China's Zheng Jie.
The seven-time Grand Slam winner lost 6-3, 2-6, 7-6 (7/5) to the two-time major semi-finalist Zheng who will take on Spain's Carla Suarez Navarro in the third round.
"This victory against the American is unbelievable," said the Chinese.