World number four Day began nine shots off the pace but made a run of five birdies in a row from the seventh and crowned a brilliant round with a 60-foot birdie putt at the par-three 17th to reach 10-under 200 for the tournament.
Hahn made three birdies on each nine in a bogey-free 64 to grab the 54-hole lead at 12 under par in his quest for a third PGA Tour victory.
Billy Horschel, the 2014 FedExCup champion, was alone in second place one shot back at 11-under after birdies at the last three, including a holeout from the greenside bunker at 17 for his 66.
Second-round leader Jason Kokrak, who led by five strokes after firing a 62 on Friday, moved in the wrong direction shooting a two-over 72 marked by a triple-bogey six at the par-three fifth hole.
Kokrak was tied for third with Day on 10 under par at the Four Seasons Resort in Irving, Texas.
Hahn said his first birdie of the day at the third hole, where he chipped in on the fly from off the green, put him in a great frame of mind.
"The chip in on three today kind of settled things down," Hahn said after the round. "I just needed one of those good breaks to happen to keep the momentum going."
Hahn could have shot even lower as he narrowly missed birdie putts on the last three holes.
Day said the key for him was locking in on his routines.
"Everything was kind of clicking," said the Australian, who won his first PGA Tour event here in 2010.
"The biggest thing for me ... was the process. The pre-shot routine was a lot smoother. The process of thinking over the golf ball was a lot smoother as well.
"When things like that happen you can kind of swing away at things and I was driving the ball wonderfully and I gave myself the opportunity to hole a lot of putts today."
Masters champion Sergio Garcia also moved up the leaderboard with a six-under 64 that put him at eight-under, four shots back.
(Reporting by Larry Fine in New York; Editing by Pritha Sarkar/Greg Stutchbury)
source: news.abs-cbn.com
