Murray made a good start, but was outplayed in the second set before finally raising his game at a vital moment in the third to go 2-1 up.
But it took the Scot a tie-break to settle the match, saving two set points after the Frenchman twice went a break up in the fourth set.
Murray, the sixth seed, will play Austria's Jurgen Melzer in the last 32.
"(Llodra) is such a tricky guy to play against, he is very good at the net," said the 21-year-old Briton.
"It was a tricky match and I knew it was going to be tough but I am glad I came through. I think everyone feels a bit of pressure in those tense moments.
"I think he served well on those big points but he did miss an easy shot and I managed to get a few returns back."



