One week after Poulter was mistakenly told he had locked up a spot at Augusta National through the world ranking, he left no doubt by winning with a clutch moment reminiscent of his Ryder Cup heroics from Medinah in 2012.
Hossler then handed Poulter the tournament at the first extra hole, the par-four 18th, where the American hit his third shot from a greenside bunker into a water hazard.
The Englishman followed up his superb 64 from a day earlier with a second successive blemish-free round, as he drained seven birdies to move to the top of the leaderboard alongside Hossler shot (69).
Poulter - who earned his fourth PGA Tour win - birdied the par-four 18th hole in regulation to force a playoff.
On Sunday, Jordan Spieth and Argentina's Emiliano Grillo tied for third place at 16 under, while Tour rookie Sam Ryder took solo fifth place at 15 under. Poulter pounded his chest five times when the putt dropped, and all Hossler could do was smile.
That set the stage for Poulter, and the 42-year-old from England lived up to his nickname as "The Postman" by delivering his biggest putt in years.
After shooting a one-over 73 in the first round, Poulter went 20 under over the next three rounds.
The event was Poulter's last remaining chance to qualify for the tournament in Augusta which starts on Thursday.
"He thought he had holed it".
He doesn't have to worry about that now after securing his first win since 2012.
Just last week, towards the end of the WGC Match Play, Poulter was told he had earned himself a spot in the Masters when in fact he had not. "I'm super excited. It's been a rollercoaster the last couple of years to be honest, to be down where I was has been tough".
"I said yesterday I wanted to beat [Ian] at his best and I saw it today", Hossler said. "She's the reason I'm here".
However, Hossler surged ahead with his birdie frenzy from the 12th to move to 19-under par, as Poulter also missed the chance to pick up a shot at the 13th, and looked on course for his maiden PGA Tour crown until the Englishman's last hole and play-off heroics.
That sort of putting wins Green Jackets, not just warm-up events. Defending champion: Russell Henley.