Kirk fired eight birdies without a bogey on the El Camaleon course designed by Greg Norman.
Kirk, whose two top-10 finishes in three starts so far this season include a runner-up finish in the Sanderson Farms Championship, fired eight birdies without a bogey on the El Camaleon course designed by Greg Norman.
"I definitely drove the ball well today," he said. "It's definitely intimidating off the tee a little bit, but thankfully I hit a lot of good ones today."
Kirk, who won the most recent of his four US tour titles in 2015, had a one-stroke lead over Colombian Camilo Villegas and Americans Gary Woodland and Ben Crane.
Mexico's Abraham Ancer was in a group on 65 that also included 2012 US Open winner Webb Simpson, Aaron Wise, Scott Piercy, Kevin Streelman and Nicholas Lindheim.
Wise's round included a hole in one on the par-three fourth, which he followed with an eagle at the par-five fifth.
"It was kind of crazy," said Ancer, whose approach shot at the third hole had hit the flagstick and spun off the green. "I got a bad break and then two great holes right after it to keep the momentum, to keep the round going."
His hole in one was with a gap wedge, he said.
"It was 118 yards or so but you have the breeze coming off the ocean there. It landed long left and spun back down. It took a while but it eventually dropped. It was pretty cool."
Ancer was thrilled to be in the hunt in front of home fans.
"I don't want to get ahead of myself and I obviously want to play well, but it would be awesome to finish up there at the end of the tournament," he said.
Defending champion Graeme McDowell of Northern Ireland endured a tough four-over 75. He had just one birdie and five bogeys and was already 12 shots off the pace and needing something special on Friday to make the cut.