Murray’s last appearance at a Grand Slam was at Wimbledon last year due to hip surgery and months of rehab.
And in the first set of his clash with Australia’s James Duckworth, Murray showed some signs of rust as he lost it in a tie-break.
But the 31-year-old responded by winning the next three sets and sealing his place in the second round.
At the end of the match, Murray raised his right arm aloft in celebration but speaking afterwards insisted he kept in control of his emotions throughout the day.
He said: “I was actually okay today. I wasn’t a little bit last night before I went to bed, but actually felt okay today.
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“I had a good warmup, and, you know, I felt pretty calm before the match.
“Obviously times in the match there was a bit of frustration there, but on the whole, I was all right.”
Murray next plays Fernando Verdasco on Wednesday and he says he can’t let the Spaniard dictate the rallies.
He said: “Fernando has an extremely heavy forehand, plays with a lot of spin. On the serve, kind of difficult sometimes to know what he’s going to do. I have played him sometimes where he’s been going for huge serves.
“And then I also played in one, he served he served like 80% first serve and kind of rolled the serve in.
“Duckworth tends to serve quite a low percentage and go for his serve.
“So they’re pretty different players. Yeah, Fernando is a great shot-maker and someone that when he’s on his game, really tough to beat. Yeah, when he’s dictating, as well, you can’t allow him to dictate too much.”