Poulter, without a win since 2012, arrived in Houston needing nothing less than victory to qualify for the Masters after missing out by a whisker when he found himself 51st in the world rankings last week. The 26-year-old gained entry via a top-10 exemption from last week's alternate-field Corales.
For Poulter it was a first stroke-play victory in America, but it was a place at the Masters which gave him most cause for celebration.
"I said yesterday I wanted to beat these guys at their best and I think I saw Ian's best today. 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".
Another great approach at the sixth yielded another birdie for Poulter to move three clear at 17-under par, before picking up another shot at the eighth, but he maintained his advantage at the top of the leaderboard following a Hossler gain at the same hole.
"He thought he had holed it".
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.
Both men played reasonable drives at the first extra hole but Hossler sent his second into the bunker before mishitting his third shot into the water, effectively leaving Poulter with three putts to win.
Poulter followed an opening-round 73 that had him packing his bags in anticipation of a missed cut with rounds of 64 and 65 to reach 14-under 202 at the Golf Club of Houston.
Poulter sank a 20-foot birdie putt at the last hole to force the playoff.
In last week's World Golf Championships-Dell Match Play, Poulter lost 8 and 6 to Kevin Kisner in the quarterfinals after he was mistakenly informed that he had clinched a spot in the Masters. "A mental switch. I was patient, I waited my time, and this is wonderful". Last week [at the Match Play] was painful and to come here this week, I was exhausted and frustrated.
"I had a good read, obviously", Poulter told NBC Sports on the 18th green after the win.