The former world number one was competing in a Grand Slam match for the first time in 14 months after hip surgery, and the 31-year-old was able to come through in four sets after dropping the opener.
The Scot will now focus his attention on trying to recover from a match which lasted three hours and 17 minutes, but the 31-year-old has indicated that his body initially felt 'better than expected'.
Murray told BBC Sport: "I played some good stuff, although spending three hours and 17 minutes on court was more than I would have liked. In the fourth set I made things a bit harder than I needed to and I also had a chance to close out the first set, but I got through it - that's good news.
"The other positive thing is I felt better than I expected to at the end of the match. When I'm going into the match I'm trying to prepare myself mentally that I'm not going to feel great physically after the match, or that my hip will feel painful, so I think about how I'm going to handle that.
"Hopefully not feeling too bad at the end of the match continues and that my body adapts to the load I'm putting it through. This is the first time I have played four sets in 14 months, so I just have to wait and see how I pull up."
Murray is scheduled to face Fernando Verdasco in the second round.