The Englishman fell behind after just the second hole, when he three-putted for a bogey while Simpson drained a par putt.
Poulter was two down when his recovery shot flew out of the greenside sandtrap at the fourth, leaving him with a monster putt.
The American carded a birdie on that hole and looked to be in control.
However, Poulter started a comeback at the fifth to apply the pressure. He was rewarded further when Simpson shanked an approach to the eighth, which meant that Poulter had two putts for the hole.
He kept his cool to lay it dead on, forcing Simpson to concede the hole.
Simpson went back ahead with a birdie at 10, but Poulter was beginning to get into the same mood he was last night, rolling putts nicely on the Medinah greens.
A birdie at 12 got Poulter back on level terms in the tight contest, that was ebbing and flowing.
Simpson was the first to crack, skewing his approach to the 17th, while Poulter drilled the green.
The European was able to sink his birdie putt to give himself a one-hole lead heading onto the 18th. He birdied the final hole to record a two-up victory.