Her six-under round gave her a chare of the lead with Brianna Do, with runaway Chevron Championship winner Nelly Korda showing no signs of slowing.
Despite playing in the windier afternoon conditions that made the fairways at El Camaleon look even tighter, Korda opened with a 68 just four days after capturing the first major of the year.
On her sixth hole of the day at the par-3 15th, Green hit a seven-iron that landed about 20 feet short of the hole and rolled into the cup. The announcers got excited because they could see it. Green, in her first year on the LPGA, did not.
"I was like, 'OK, great shot. Phenomenal.' Grab the putter - normally hit the green, grab the putter, it's a cool effect.' Then we're walking up and I'm looking at the green. There is no ball," Green said.
She was momentarily embarrassed by having to hand her caddie the putter and take a wedge to chip. Her caddie repaired the pitch mark, glanced in the hole and saw her golf ball, which he knew by it being marked with a cross.
She thought he was joking.
"I walk up there and all I could see was the cross. I was so excited," Green said. "Yeah, thought I just went way left. But whatever. Good bounce."
And it was a great start. Along with her hole-in-one, Green had five birdies and went out in 30. She was slowed by a bogey on her final hole but had few complaints.
Do was first off in the afternoon, before the wind reached full strength, and opened with four birdies in five holes. She also dropped a shot at No.9, then played the back nine bogey-free with a trio of birdies to join Green.
Do said it was windy in her US Women's Open qualifier a few weeks ago and it prepared her for the wind coming off the Gulf of Mexico.
"I think for some reason playing in the wind helps me kind of just play golf, instead of like playing a golf swing," Do said.
Korda returned to No.1 in the women's world ranking last week at The Chevron Championship, a performance so dominant she led over the final 57 holes and won by five.
She stuck to her commitment to Mayakoba, where she is the only player from the top 10 in the world.
Australia's Robyn Choi is one behind Korda. Her 69 included five birdies and two bogeys.
Choi enjoyed a run of three consecutive birdies starting on the fifth, but then made bogey on the eighth - her second-last hole on the day - to drop her into a tie for 10th.
Compatriot Gabriela Ruffels shot 70 to be tied 17th.
After a disastrous start where she bogeyed two of the opening three holes, Ruffels fought back with birdies on the fifth, eighth, 10th and the last to climb up the leaderboard.
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