The 34-year-old American, the PGA Tour's first player of Samoan and Tongan descent, fired an eight-under par 62 to finish 36 holes at Memorial Park on nine-under 131.
"I've played some nice golf the first couple days and the game's in a good place," Finau said. "Just don't overthink it, get some rest, be properly prepared, properly rested for the weekend."
World number one Scottie Scheffler, seeking a third victory in as many starts, was second on the course at 6-under.
Finau started on the back nine and made a 10-foot birdie putt at 13, a birdie at the par-5 16th after reaching the green in two and a 13-foot birdie putt at 18, followed by his lone bogey of the day at the first.
Finau barely missed on a 31-foot eagle putt at the par-5 third and tapped in for birdie, then sank a 27-foot birdie putt at the fourth.
He added 30-foot birdie putts at the sixth and par-3 seventh then holed out from just inside 40 feet to eagle the par-5 eighth and at the par-3 ninth rolled a 16-foot birdie putt past the hole to miss out on 61.
"I knew what it was for -- 61 would have been my lowest on the tour and the course record," Finau said. "I knew I was going to give it a run. I wasn't going to leave it short.
"I hit a good putt and it was barely too low. I thought I hit it hard enough for it to stay on the line."
Finau fired a second-round 62 to win the 2022 Houston Open, when the event was played in November. The tournament went unplayed last year due to the PGA shift to a calendar-year season, giving Finau a chance to defend this week and compare his 62s.
"I think my 62 in the fall was actually better," Finau said. "The golf course can yield some birdies from the rough because the rough is so much shorter.
"When I (first) shot 62, I hit 14 out of 14 fairways and that was quite impressive. But 62 is good anytime of the year and I'll take the one today."
One thing Finau says is better this year is his driving, attacking the course to avoid fairway bunkers.
"I definitely have been more aggressive off the tee just in some bunkers I'm trying to take out of play," he said. "Last year I couldn't take them out of play. I just wasn't swinging fast enough."
Finau seeks his seventh career PGA Tour title, his first since last April's Mexico Open.
