Shubhankar, 22, who catapulted into global fame by leading after 54 holes on his PGA Tour debut at the 2018 edition, is now tied 19th on a day, when Rory McIlroy (63) and Dustin Johnson (64) pulled themselves well clear of the field at the Par-71 Chapultepec Golf Club.
Last year Shubhankar finished tied ninth at the $10.25 million tournament.
Thai star Kiradech Aphibarnrat produced his best opening round of the year on the PGA TOUR, carding a three-under 68 for a share of the seventh spot.