The Thai star briefly led the World Golf Championships-Mexico Championship after 10 holes of his second round at the Club Golf de Chapultepec but found himself on the bogey train with three dropped shots over his last eight holes.
He was at 11-under 131, two ahead of Masters champion Sergio Garcia, Xander Schauffele and Rafa Cabrera Bello.
Ten players were within four shots of the lead going into the weekend, a group that includes defending champion Dustin Johnson, who holed a wedge from 112 yards for eagle on the ninth hole and shot a 66.
Sharma entered the week already ranked first on the European Tour after two early-season victories, in South Africa and Malaysia.
"I didn't really put any pressure on myself before I came here. I'm really enjoying it and that's when I'm able to play my best".
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The Masters has a tradition of occasionally inviting a non-exempt Asian player, raising the intriguing possibility that Sharma might yet receive a prized summons, even if he doesn't qualify automatically.
"When I came out on Monday I was so overawed by just so many people being here and so many kids coming up to me and asking for autographs", he told PGA Tour radio after his round.
"I knew I had to hit a great 3-wood", Sharma said.
"I just kept the ball in play throughout the day", Sharma said.
Starting his day on the 10 hole, the Thai made birdies on 13 and 18 and eagled the par-5 15 hole after holing a 44-foot putt from the fringe. So I just wanted to have fun, and yeah, I've had a lot of fun. It's my first WGC and I was happy that I'll play four days because I missed the cut in the last two events that I played. "Was pretty happy with the way I drove the ball and I think that was the key". "Just playing well here this week will get my closer to my dream".
A win or runner-up finish for the 25-year-old Greystones man would have pushed him into the the world's top 50 and sealed a spot at Augusta in April.