The American left-hander returned to the course early on Saturday, after not even playing a shot on a storm-hit Friday, and found himself four-over par for the tournament and three strokes short of the projected cut with nine holes to play.
He picked up two birdies in a blemish-free eight holes and walked to the par-five 18th tee knowing a birdie would keep him in the tournament.
However, despite hitting what he described as a "perfect" drive, his five-wood approach shot skewed left over the lake and nestled in the rough on the edge of the adjoining 10th hole.
Mickelson surveyed the scene and opted for a high-risk chip shot that soared between the 'V' of two palm trees in his path and scuttled up the green to halt around six foot from the cup.
The American calmly slotted in the birdie putt, much to the delight of the packed gallery.
"I hit one of the best tee shots I have hit all week and one of the worst second shots I have hit all week with the five wood. I don't even know what happened there," he told reporters.
"It was one of the best chips... I had to go through the trees and run it up the hill. I hit it really well and made birdie and hopefully have given myself a chance."
Despite languishing 10 shots behind clubhouse leader Thomas Bjorn (nine-under) with two rounds remaining, Mickelson is still hopeful of climbing into contention after flirting with ending his tournament after just 36 holes.
"It's a tough course for me to make birdies, but I am trying and hopefully, I'll make a few putts this afternoon. To get into position on Sunday, I need to shoot a low one," he added.
"I drove the ball well off the tee and gave myself some chances into the greens. I didn't hit the best iron shots but wasn't far off. I should now be a little more aggressive and be able to make some birdies." (Editing by Amlan Chakraborty)
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