The American, who on Sunday came from five behind to win the 3M Open and set the tournament record for the largest final-round comeback in Minneapolis, was tied with playing partner Taylor Pendrith of Canada at 21 under going into the final day in Detroit.
Finau has yet to make a bogey this week at Detroit Golf Club, while Pendrith, who leads the field with 25 birdies, managed a 66 thanks to the late spurt.
"Taylor's playing some great golf," Finau said after play ended on Saturday.
"I can't say we pulled away from the guys, this is the type of golf course where someone can shoot 8, 9, 10 under, but if we put together a good round tomorrow, might be a two man race and I'm looking forward to the challenge again."
"I'm just hitting a lot more fairways than I'm accustomed to or than I have in the past. This golf course really opens up to you if you hit it in the short grass and it definitely has for me these first three rounds.
"I feel like I hit it as good as I've hit it from tee to green last week, so I think I've definitely elevated that part of the game.
"It's nice to capitalize on some of the putts."
Cameron Young also carded a 65 to finish on 17 under followed one shot back by Germany's Stephan Jager, with FedEx champion and world number four Patrick Cantlay - the top-ranked player - six off the pace.
Englishmen Matt Wallace and Danny Willett both shot 69s to respectively be 11 and 12 strokes back from the leaders, their countryman Callum Tarren was at seven under with Scotland's Russell Knox a further stroke back followed by former world number one Luke Donald on two under.