After Hossler ended with a seven, Poulter made par to seal a win which takes him up to 29th in the World Golf Rankings.
The Englishman slipped into full Ryder Cup mode, dramatically holing a 20-footer to enforce a play-off and then prevailing on the first extra hole.
The win was all the more remarkable considering the Englishman was tied for 123rd place after Thursday's first round, the lowest 1st-round position by a PGA Tour victor in the last 35 years.
The world No 4, without a worldwide victory since claiming the Open Championship, posted a five-under 67 to get to nine under and stay in touch with midway pacesetter Beau Hossler.
Ian Poulter, a player utterly dejected when sharing 123rd place after the opening round of the Houston Open, a player wrongly informed he had qualified for the Masters before falling to a heavy defeat at the WGC Match Play and a player who needed to convert a birdie putt from 19ft to prolong that Augusta dream, is a victor once again.
"I said yesterday I wanted to beat these guys at their best and I think I saw Ian's best today".
"I was patient, I waited my time and this is unbelievable". He went with the same Odyssey #7 that he used to help inspire Europe's stunning comeback at the 2012 Ryder Cup at Medinah.
"I hit a great putt, good read and it obviously was very helpful seeing his putt", Poulter added.
Attempting to generate a lot of spin with his third shot out of the sand, Hossler flew the green and his ball wound up in the water, all but sealing the victory for Poulter, who could have taken four putts from 33 feet to win the tournament.
Poulter finished the day tied with American Beau Hossler on 14 under par ahead of the final round, knowing that a only victory will earn him a place at Augusta next week.
Ian Poulter, who said last week after the WGC Dell Match Play that he wasn't sure he was going to play this week, showed up.
"I was frustrated, not really with my play on Thursday but the result - it wasn't good".
Spieth, a native of Dallas, Texas, played at Texas from 2011-2012 before going pro.
He told the Golf Channel: "I had to pack my suitcase because potentially I was flying home on Friday and you never like to do that".
Severe weather possible Tuesday
The cold front will sweep across the southeast Tuesday through Wednesday , arriving in Middle Georgia early Wednesday morning . The Storm Prediction Center has elevated us to the "Moderate" category for severe weather through the end of the day.
`Hill Street Blues' Creator Steven Bochco Dead at 74
The 10-time Primetime Emmy Award victor was also behind comedy-drama " Doogie Howser , M.D" starring Neil Patrick Harris . Among the accolades that Steven received during his career are 10 Emmys and four Peabody Awards.