Hossler, who also shot 67, ran off four straight birdies on the back nine to take a one-shot lead going to the final hole.
Using the same putter he wielded so effectively to lead Europe to victory in the 2012 Ryder Cup, Poulter sank a 20-foot birdie putt at the last hole to force the playoff.
A stunning shot from the fairway bunker on the second hole earned Poulter his first gain of the day when he dialled in to six feet to take the outright lead on 15-under par before landing an approach to three feet for a tap-in birdie at the fourth to move two shots clear.
A 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 in clutch fashion over PGA Tour rookie Beau Hossler.
"I guess I should never listen to other people", Poulter said. That's as low as I've ever been, that's as far down the world rankings as I've been, questioning whether you've got a Tour card or not - it isn't very good.
"Last week was painful", Poulter said. "My first strokeplay win in the States, and to do it with the Masters on the line is unbelievable".
Ireland's Paul Dunne was among four players tied for third place at 12 under after shooting a three-under par 69.
"It's been a rollercoaster the last couple of years to be honest, to be down where I was has been tough".
NOTES: Phil Mickelson shot bogey-free 67 Sunday to finish in a tie for 24th at 10 under.
"My tee-to-green stats have been fantastic", he said ahead of the WGC, "but my putting has to catch up, because if I get it back to where it was from 2009 to 2012 it will be very, very exciting".
Knowing it would take a near-perfect shot to reach the back-left hole location, Hossler overshot the green and found the hazard, leading to a triple-bogey that ended his tournament hopes.