
In pursuit of his 35th PGA Tour title, the American left-hander mixed three bogeys with a spectacular eagle at the opening hole to reach the turn in one-over-par 36.
That left him at 15 under overall, with compatriots Fred Couples and Steve Stricker and Argentina's Andres Romero tied for second place.
Twice champion Couples and Romero had also played nine holes in generally overcast conditions at Riviera Country Club while Stricker had completed 10.
Four ahead overnight, Mickelson briefly stretched his lead to six when he holed a 34-foot putt to eagle the par-five first, punching the air with his left fist in celebration.
However his playing partners Couples and Romero both birdied the hole to trim his advantage to five.
Mickelson then bogeyed the next two holes, duffing a chip from just off the green at the par-four second and hitting a tree with his tee shot at the third to drop back to 16 under.
Couples, who struck a superb approach to three feet at the par-four third, tapped in the putt to get to 14 under.
Although Couples bogeyed the tricky par-three fourth, three-putting from just off the green, Mickelson again stumbled at the seventh where he missed the fairway off the tee and overshot the green with his approach.
Mickelson was fortunate not to drop another stroke at the eighth, where he ended up in trees off the tee and struck branches with a bold recovery through a narrow gap.
He narrowly missed a 16-foot birdie attempt on the ninth green to enter the back nine two ahead of the chasing pack.
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