The Wimbledon champion swept into the second round with a 6-1, 6-1, 6-3 rout of Japan's Go Soeda as he works his way to full match fitness after surgery last September.
The fourth seed was never in trouble against the 112th-ranked Soeda, breaking the Japanese player's service seven times and not having a break point against his own serve.
Murray, who lost to Novak Djokovic in last year's Australian final, said it was the best he had felt on court for 18 months, following his surgery in September.
"That was the whole point of having the surgery. So if I was still in pain and stiff and sore then I'd be a bit worried about the next few years.
"But I'm hoping it was the right decision. I felt freer today than I did for the last 18 months.