Poulter only needed a par on the first playoff hole, as Hossler had a complete nightmare, with his first two shots ending in bunkers and his third in the water.
The stars aligned for Poulter at the final hole in regulation play on Sunday, when Hossler grazed the hole with a birdie attempt that would have clinched victory.
And it was down to two when Poulter suffered his first/only wobble at the par three ninth.
Poulter got his third win on the PGA Tour, and his first in USA since the Match Play in 2010.
After shooting a one-over 73 in the first round, Poulter went 20 under over the next three rounds.
Poulter then lost his last eight match to Kevin Kisner 8&6. "I had packed my bags to leave on Friday night, and had a mental switch", Poulter said. I haven't won a strokeplay event in the United States before and to do it this week is fantastic.
"I haven't won a stroke play event in the States, so to do it this week, after the disappointment of last week, to know I'm going to Augusta, to do it in true fashion is fantastic", the 42-year-old Englishman told NBC.
Argentinian Grillo bogeyed the last to finish alongside three-time major championship victor Spieth at 16 under, with American Sam Ryder one shot further adrift.
The Englishman led for the majority of the final day's play, but Hossler registered four successive birdies on the back nine to put himself at the top of the leaderboard heading into the closing holes.
Both players parred Nos.
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.
"I'm going to have a good day's rest tomorrow, I will not be venturing to Augusta until Tuesday". "I thought Beau hit a good putt, I thought he holed it". Martin Kaymer is playing for the first time since Riviera because of an injury. Isner, 32, became the first American man to win the tournament since Andy Roddick in 2010.
"This one's for Katie, my wife", Poulter said. "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".