At 11-under 202, Lahiri was seven shots behind the leader, Gary Woodland (66). Woodland has had rounds of 64-65-66 and is now one shot clear of Pat Perez (62) who moved into reckoning with a superb nine-under 62.
Lahiri, who was in contention at the CIMB Classic last month, got off to a flying start with five birdies in first eight holes.
"I have been playing solid and I hope I can have a strong finish on Sunday. I had a few putts that refused to go on the back, so was a little disappointed not to shoot a lower score," said Lahiri.
"The golf course has a few birdies to offer if you can strike it good. I am happy to put myself in a good position going into Sunday, so I will try my best to make it count," added the 29-year-old Indian, whose best in last months has been a second at Hero Indian Open and third at CIMB Classic.
Woodland finished with a 5-under 66 to reach 18-under 195 on Mayakoba's Greg Norman-designed El Camaleon course. He won the last of his two TOUR titles in 2013.
Pat Perez was second after a 62. Scott Piercy was 16-under after a 66, Seamus Power (64) was 15-under, and Webb Simpson (69) followed at 14-under. Defending champion Graeme McDowell was 8-under after his second straight 65. He opened with a 75.
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