Hovland is chasing a rare PGA Tour feat of three consecutive wins of the same tournament, something that has only been achieved by three other players in history, and began his quest by firing a six-under-par 65.
That left him three shots off the early pace set by American Gordon, whose opening 62 was the lowest round of the day.
Gordon made eight birdies and an eagle against a lone bogey to lie one shot ahead of compatriot Russell Henley at El Camaleon in Riviera Maya, Mexico.
"I was in a fairway almost every hole," he said. "So you have a lot of opportunity to hit the ball close. And with the putter hot, it was a pretty smooth day.
"It's just really about managing my expectations and my emotions, so I feel like I did a good job of that today. Kind of let the round come to me and I putted it really well."
Sharing third a shot behind Henley were Italy's Francesco Molinari and Americans Scott Piercy, Sam Ryder and Harris English.
Two-time defending champion Hovland of Norway follows in a tie for seventh alongside reigning Masters champion Scottie Scheffler, who would overtake Rory McIlroy as the number one-ranked player in the world if he wins this weekend.
"I felt pretty efficient. When I hit really good shots, I hit it really close to the hole," said Scheffler, who avoided any blemishes on his card. "I had a lot of tap-in birdies, which is nice.
"Any time you can stay bogey-free, it's a really nice day."
Hovland stumbled a bit on the back nine - his front - after twice finding the water and making bogey, but he also made two birdies during that stretch before adding four more gains and an eagle after the turn to recover nicely.
"Didn't hit any iron shots in the water on the front so that usually helps," Hovland said. "I played pretty well. It was just two shots that cost me three.
"I kept telling myself, yeah I'm a little bit behind pace but if I just keep playing well I can get back into it and I certainly did that."
"I'm chipping the ball pretty well. Putting good again. It's about minimizing the mistakes."