The Europeans got off to a bad start, with stray approaches at the first and missed putts at the second, to find themselves two down after the first two holes.
Poulter found the bottom of the cup for a birdie at the fourth to halve the deficit, but the American restored their two-up cushion with a birdie at the par-five seventh hole.
McIlroy kept Europe in the match with a superb two at 13, before Dufner's missed putt at 15 saw Europe get themselves back on level terms, thanks to a birdie from Poulter.
Events swung dramatically in Europe's favour at the 16th, when Poulter sunk another birdie putt to put pressure squarely on the shoulders of Dufner.
The American could not find the hold and Europe found themselves one up with two holes left to play.
Poulter made another birdie at the 17th, forcing Johnson to putt to stay in the match. Thge American made no mistake from inside five feet to take the match to the final hole.
Dufner's superb approach to the final flag meant that McIlroy and Poulter had to at least give themselves a chance of a birdie, which they did.
After Dufner had tapped in for birdie, Poulter was forced to hole yet another tricky putt to protect the point and keep European hopes alive.
He found the centre of the cup to send the visiting fans into raptures and reduce Europe's deficit to four as they head into the singles.