Hatton, whose lone win on the PGA Tour was at the 2020 Arnold Palmer Invitational, joined the LIV series in January, with his best finish so far a tie for fourth.
Starting a stroke back of first-round leader Abraham Ancer, he birdied six of his final seven holes for a 13-under 129 total.
John Catlin (66) was at 10 under in his second LIV Golf event.
Fresh from his second US Open triumph, Bryson DeChambeau (66) was tied at nine under with former world No.1 Jon Rahm (63).
Rahm missed last week's US Open and withdrew from the previous LIV Golf event with an infection on his left foot. On Saturday, he opened with a bogey before finishing with nine birdies.
The Spaniard said he was playing nearly pain-free after being uncertain whether he would be able to walk 18 holes when he flew to Tennessee.
"I never really questioned not being able to swing (the club), and that's what made a difference," Rahm said.
Carlos Ortiz, who won LIV Golf Houston, shot a 66 and was tied with Australia's Cameron Smith at eight under.
Smith carded five birdies, as well as a double on the par-5 11th hole on his way to a second-round 65.
DeChambeau has had little sleep since winning the US Open for the second time at North Carolina's Pinehurst No.2 last weekend.
On Saturday, he birdied four of his final six holes and showed few signs of exhaustion - especially after his tee shot at the party hole, the par-3 15th, when he ran around high-fiving fans circling the green.
"I just blacked out, I have no idea," DeChambeau said.
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