Ryder's bogey at the short 14th gave Poulter some wiggle room, and normal service was resumed on the 11th, as he holed a seven footer to move three clear again.
The top 50 at last Monday's cut-off earned exemption to Augusta, and Poulter was so dejected after being initially misinformed he was in the Masters field that he considered skipping Houston.
"I did think I'd made it", Hossler said, "but it hung out there".
Victory would be particularly sweet for Poulter, who was told last week that he had qualified for the Masters after reaching the last eight of the WGC Dell Technologies Match Play, only to be told just before his quarter-final that there had been a miscalculation. "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 wonderful". He went with the same Odyssey #7 that he used to help inspire Europe's stunning comeback at the 2012 Ryder Cup at Medinah.
Poulter kept his nerve as he putted from 20 feet which prompted a passionate show of emotion as he beat his chest in celebration.
In other news from the tournament, Jordan Spieth is back in form, as he finished third, with a final day round of 66.
He then took the title on the first extra hole when Hossler chipped into the water from a bunker before making a triple bogey.
Poulter's third victory on the PGA Tour followed previous wins at World Golf Championships events - the 2010 Match Play and the 2012 HSBC Champions in Shenzhen.
"To come here this week, I was exhausted, I was frustrated", said Poulter, who packed his bags after shooting 1 over on Thursday, assuming he would miss the cut.
"I was frustrated, not really with my play on Thursday but the result - it wasn't good".
"I got the best of Ian Poulter today and he got the best of me", said Hossler. 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.
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