Making his World Golf Championships debut, Sharma opened with a round of 65 on Thursday and stormed home in 31 to follow up with a five under par 66.
American Xander Schauffele is tied in second place with Spanish pair Rafa Cabrera Bello and Sergio Garcia.
Among those is overnight leader Louis Oosthuizen, defending champion and World Number One Dustin Johnson and Thai star and Perth World Super 6 champion Kiradech Aphibarnrat.
Sharma entered the week already ranked first on the European Tour after two early-season victories, in South Africa and Malaysia.
He said he had misjudged the distances of some of his iron shots in the thin air, but not enough to cost him a bogey.
"Everything has happened so fast for me", Sharma said. Things are starting to heat up in Mexico City.
"I worked all my life to come and play at a high stage like this", said Sharma, who turned pro when he was 16.
ICE raids result in arrest of more than 150 Bay Area residents
In the Bay Area, 864 undocumented individuals "remain at large" in part because of Schaaf's warning, ICE deputy director Thomas D. Immigration and Customs Enforcement (ICE) says "created another magnet for more illegal immigration".
Sharma hit a 3-wood on his opening tee shot to 2 feet for a tap-in eagle and overcame consecutive three-putt bogeys. "I couldn't be in a better situation".
Hardly anyone knew much about Schauffele a year ago before he played well at the U.S. Open, and then won the Greenbrier Classic and Tour Championship.
"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.
"But I put in a lot of work to get my yardages dialled in and I think that's very important here". 'I just wanted the first round to get out of the way, said Sharma, who has been hooked on golf ever since he was introduced to the game by his father as a six-year-old. The Spaniard was flawless, holing an eagle and four birdies at Club de Golf Chapultepec.
Key to his success was an eagle at the par-five 15th hole as he took command of the first of the four WGC events this year. He had only one birdie on the back nine and started the front nine with five straight bogeys before finishing the day at 75, putting him at two under for the tournament and dropping him 27 spots.
England's Chris Paisley went from six-under-par midway through his second round to two-under-par after dropping four shots in three holes on his back nine.
- Leicester City's Shinji Okazaki could return to squad for clash against Bournemouth
- Kabul vehicle bomb attack: Two Australian nationals wounded says Julie Bishop
- U.S. support for Saudi Arabia in Yemen must end, senators say
- President Buhari condemns 'despicable' attack on humanitarian aid workers
- Does WWE have a Brock Lesnar problem ahead of WrestleMania 34?
- Seattle Seahawks Actively Trying To Trade Michael Bennett
- Companies take gun control into their own hands
- Central Virginia bracing for high winds
- Oscars Best Picture Mistake in 2017 - What Went Wrong, What Happened Next?
- Google's Slack Competitor Hangouts Chat Launches For Businesses Using G Suite