Triplett had an eagle and seven birdies at Indian Wells en route to a 9-under-par 63 and a four-day total of 26-under 262.
Playing Bermuda Dunes, Mickelson had a seemingly comfortable four-shot lead midway through the back nine. But the lefthander bogeyed the 16th hole just around the time Kenny Perry went eagle-eagle-birdie at La Quinta to get within a stroke.
Mickelson ended up shooting a 5-under 67, but Perry closed in with a 64.
Jay Haas, last year's runner-up, parlayed a bogey-free 5-under 67 into sole possession of fourth place at 264.
Ben Crane (68), Skip Kendall (66) and Danny Ellis (64) are tied for fifth, three shots off the lead.