The world No 2 was playing his first competitive match since his Davis Cup win over Guido Pella a fortnight ago, where he suffered a thigh injury, and he got back in the groove with a 6-2, 7-5 win over Andreas Seppi.
There were doubts whether the Scot would compete in the 2008 Olympics host city after the injury in Glasgow came at the end of a punishing schedule over the summer, which saw him lose just four matches since the end of May.
But, with a shot at the No 1 ranking in mind and no Novak Djokovic in the draw, Murray stuck to his itinerary and got the job done in straight sets against the Italian.
After an even start, Murray, the top seed, took the game by the scruff of the neck by reeling off four successive games which earned him the first set.
A double fault handed Seppi a break early in the second set, but the British number one was able to recover the situation and after breaking back to take it to 2-2, he delivered another, decisive blow, at 6-5 to claim victory.
He will play Konstantin Kravchuk or Andrey Kuznetsov in the second round, with a potential match-up against British No 1 Kyle Edmund in the quarter-finals.