Wise, who qualified for this week's PGA Tour event by finishing in the top 10 at the Shriners Hospitals for Children Open on Sunday, ended the opening round two shots behind the pacesetting Chris Kirk, who racked up four birdies on each nine.
Colombian Camilo Villegas and Americans Gary Woodland and Ben Crane carded 64s while defending champion Graeme McDowell of Northern Ireland launched his title defence with a struggling 75.
Oregon resident Wise, making only his sixth career start on the PGA Tour, was delighted to bounce back in such dramatic fashion after suffering an unfortunate setback with his approach at the par-four third.
"I had a wedge into three and hit the pin and it (his ball) came all the way back off the green, which I thought was a really bad break," Wise told Golf Channel.
"But then I walked over to four tee and made it and walked over to five and hit two great shots and made about a 30-footer for eagle," said the American, who achieved his ace at the fourth with a gap wedge from 103 yards.
"So it was kind of just all the momentum went on my side and I was able to keep it bogey-free throughout and had a pretty clean scorecard."
Asked to describe his hole-in-one, Wise replied: "I knew it (the breeze) was coming in off the left hard because you are going right back into the ocean there.
"I landed it long left and it spun back down the hill, and it probably ran for three or four seconds and eventually caught the edge and went in. It was a pretty cool feeling."
(Reporting by Mark Lamport-Stokes in Los Angeles; Editing by Frank Pingue)
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