He was one stroke in front of England's Chris Paisley and American Xander Schauffele, the US PGA Tour's 2017 Rookie of the year.
Defending champion Dustin Johnson emerged from a roller-coaster round with a two-under par 69.
There was a 33-minute delay due to lightning but the round was completed after play resumed at 17:52 local time (23:52 GMT). His highest finish in a WGC event is 4th.
Instead, Thursday at Chapultepec Golf Club delivered a mixed bag of compelling, if not little-known, players and just as many out-of-character performances.
Paisley opened with back-to-back birdies and added two more at the fifth and sixth, seizing a share of the lead on five-under with a birdie at the 10th, where he rolled in a 10-footer.
"The ball was below my feet [in a fairway bunker], it was not sitting great, and I didn't really have anywhere to miss it coming out of where I was hitting it", he explained. I was also really happy with the birdie I made on 18.
"On the first hole it's just about hitting the right shot and positioning yourself".
Consider Paisley, who describes himself on his Twitter account as a "diminutive golfer from Newcastle, the anti-DJ".
"It's the biggest tournament I've played in by a long stretch", Paisley said.More news: How to Watch Real Madrid vs. Getafe
"I gave myself a lot of chances but they're tough greens to putt on and to hole as many putts as I did, I'm delighted".
Justin Thomas didn't carry over his best form from last week's playoff victory at the Honda Classic.
Former world number one Jordan Spieth carded a one-under-par 70, which included four birdies and three bogeys. I'm consistently working hard and I feel like I'm always doing the right things.
"I didn't want to come here and just be happy to be part of it and just make up the numbers", he said.
Rising Indian golfer Shubhankar Sharma savoured a dream debut at the World Golf Championships-Mexico Championship as he fired a sizzling six-under 65 to grab the tied second place after the opening round.
Louis Oosthuizen takes an early lead at the WGC-Mexico Championship on Thursday. 3, 4 and 5 in 4 over par to plunge down the leaderboard.
Oosthuizen has won just once on the PGA Tour, claiming the 2010 Open Championship at St. Andrew's.
Hot on his heels are a trio of players getting their first taste of World Golf Championship play.
But then, while it might be billboards that sell tickets and generate interest, it's the names on the leaderboard that count once the competition has started, whether that lineup includes a superstar cast or not. By comparison, neither Paisley nor Sharma even have pictures or bios to go along with their scorecards.