Leishman pitch from 45 yards short of the 18th green rolled out to 3 feet, and he made the par putt for a 3-under 69.
Kevin Kisner had a three-shot lead at the turn, but he didn't make a birdie over his final 11 holes.
Rory McIlroy made a late charge and tied for the lead with a wild birdie around a tree and over the water on the 16th hole, only to three-putt the final hole from 30 feet.
It was the first Arnold Palmer Invitational since the death last September of the tournament host.
