Mickelson, who had nine birdies and an eagle in the round, is tied with India's Gaganjeet Bhullar, who had a 66, at 10-under 206 entering the final round.
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"I just love the fact I am in contention and have an opportunity in my first tournament of the year here in Abu Dhabi," Mickelson said.
Mickelson barely made the cut after shooting an opening-round 73. His second-round 70 put him two shots ahead of the cut line, though.
"The biggest thing for me is that each day as the tournament has progressed I have felt a lot sharper and sharper," Mickelson said.