The 26-year-old Yu made a 15-foot birdie on the 18th hole for a closing five-under 67, and he birdied it again from six feet the clinch the playoff at the first extra hole.
In his 200th PGA Tour start without ever winning, American Hossler shot a 68 after only salvaging a par at the 18th as he tied with Yu at 23-under 265.
Hossler was left off the tee in the playoff and could only make par again after punching out from below trees.
Yu's victory sends him to the Masters and the PGA Championship for the first time. He also will start his season at Kapalua for The Sentry, a gathering of PGA Tour winners in 2024.
"I've been dreaming this moment since I was five," Yu said. "This is the dream for all golfers, to win on the PGA Tour. I did it today. I'm thankful for my parents. Without them, I couldn't have done that."
Yu was nearly forgotten for most of a final round that appeared to be a duel between Hossler and fellow American Keith Mitchell.
Mitchell had a 35-foot birdie putt to win the title on the 18th and it grazed the left edge of the cup. But he missed the four-foot comebacker for par, shot 70 and missed the playoff.
Mitchell tied for third with former US Open champion Lucas Glover (66), who played the last six holes in five-under par - including pitching in for eagle on the par-4 15th.
Hossler gave credit to Yu for his play in the clutch.
"Even though I didn't have my best stuff on the back nine I grinded really hard," Hossler said.
"Hit some really quality shots under the gun, and that's all you can do. Obviously, Kevin played a beautiful hole in the playoff."
Mitchell might have the most regrets in search of his first win in five years.Â
He was two shots ahead with five to play when he failed to birdie the par-5 14th or the reachable par-4 15th. He still had a putt to win, and that's where it all went wrong with a three-putt bogey.
"I hate that I finished with a three-putt," Mitchell said. "Felt like I grinded all the way to the end and gave the first putt a really good chance."
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