Rose appeared set to be the leader heading into the final round when he moved to 5 under for the day and 13 under for the week - two clear of Finau - with his sixth birdie of the day at the 16th.
"Definitely feel like I let one get away", the Lehi resident said as he walked off the 18th green after Sunday's playoff.
"There's 18 more holes to play and it's a world class field". He added another birdie on the 9th, his last. "You practice, you play hard, and you do everything that you can to get in this position and it honestly is a great feeling to pull it off".
"I didn't have a lot going my way for the first half of the day and Rosey was making his run".
"I'm really pleased. I played nicely and was happy with the way I finished".
Finau boosted his hopes of a first European Tour win at just the 20th attempt with a strong finish.
On the PGA Tour, West Waterford's Seamus Power made two birdies and a bogey in a one-under 71 in the Sanderson Farms Championship to find himself eight shots behind rookie Cameron Champ at a wet and windy Country Club of Jackson, where he slipped from tied third to 18th after a final-round 75 a year ago. In his opening fourballs match with Brooks Koepka, the USA team looked to be in big trouble until Finau's tee shot on the 16th hole hit off the railroad ties framing the green and settled 3 feet away, crucial to winning the match.
Matt Fitzpatrick was two-over after four holes but shot a 67 to sit alone in fourth as current Race to Dubai champion Tommy Fleetwood, Thai Kiradech Aphibarnrat, Spaniard Rafa Cabrera Bello, American Billy Horschel and Taiwan's CT Pan shot 68s. It led to a double bogey and cut his lead to one shot.
But he triple-bogeyed the 14th after finding the water before picking a shot back up on the last. It led to a double bogey and cut his lead to one shot. Xander Schauffele was another shot behind after a 71, while Patrick Cantlay wasted a good birdie chance on the final hole and had to settle for 68.
Rory McIlroy dropped 16 shots off the pace at the WGC-HSBC Championship in Shanghai after an error-ridden five-over 77 in Friday's second round.