The 21-year-old Sharma ground out a two-under 69 which included a clutch 13-foot par save on the 18th hole at the Club de Golf Chapultepec as he held off the likes of Phil Mickelson (65), Tyrrell Hatton (64), Sergio Garcia (69) and Rafa Cabrera Bello (69).
World No. 1 and defending champion Dustin Johnson shot a 68 to share sixth place, three behind Sharma, who has literally taken the world by storm with a measured and composed performance this week.
"Obviously a dream come true for me to be playing in this tournament and obviously leading, that's just fantastic. Really happy with the way I played today, stuck in there," said Sharma, who is making his debut appearance in the World Golf Championships.
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Sharma broke through with his maiden victory at the Joburg Open in December and followed up with another triumph at the Maybank Championship in Malaysia last month where he came from four shots back to win with a closing 62.
In his biggest test yet, the current No. 1 on the European Tours Race to Dubai and Asian Tours Habitat for Humanity standings will be grouped with five-time major winner Mickelson and Englands Hatton as he bids to become the youngest player to win a World Golf Championships tournament and only the second Asian after Hideki Matsuyama of Japan to do so.
"Obviously Phil is a legend in the game of golf and I've seen him on TV for as many years as I can remember. You know, I met him for the first time today and it's great that I'm paired with him tomorrow. It will be a lot of fun."
Sharma has gone about his business in Mexico so quietly that when he sheepishly approached Mickelson, a 42-time PGA TOUR winner, at the practice putting green to introduce himself prior to his third round, the World Golf Hall of Famer initially waved him away thinking he was a journalist.
"Then he just realised and said, 'So sorry, I thought you were media,' and he said hi, I said hi. Then he made a few putts and he came back to me and said, 'Have a good day'.
"It was nice," recounted Sharma, who turned professional at 16 as his father felt it was the best way to get better at the game.
When he was younger, Sharma, his father Col Mohan Sharma, who is here this week, and some friends would stay up early into the mornings in India to watch the live telecasts of PGA TOUR tournaments and the majors.
"The best I think was when Rory (McIlroy) won the U.S. Open. It went on until 6:00 in the morning back home. I remember I was so inspired that I didn't sleep, I just went straight to the range and hit balls for two hours. It's great for kids like me back then."
Asked if he ever envisioned himself holding aloft a major or World Golf Championships trophy, he replied: "Every time, every time watching these majors.
If he keeps making putts and performing the way he has been at the WGC-Mexico Championship, Sharma will be the one inspiring the next generation of Indian and Asian golfers.