The Northern Irish duo fell behind on the second hole, but then put together a string of four straight birdies to take a one-up lead after six holes.
Furyk and Snedeker toiled on the front nine and found themselves three down as they approached the 13th tee.
However, the momentum then swung towards the Americans, as was the case all over the course. Snedeker had a put on the 14th to cut the lead to one, but he could not find the cup from the fringe.
McDowell still had to hole a 15-footer for a half, and he held his nerve to do exactly that.
The Americans did not relent though, and punished McDowell for a tee shot that he dumped into the water on the 15th. Snedeker holed a putt that saw their deficit reduced to one.
It was all square by the time the players reached the penultimate hole as McDowell missed a par putt, and the Americans were firmly in the ascendancy.
McIlroy found a straight drive just when he needed one on the final hole, while Snedeker was way off target, forcing Furyk to pitch back out onto the fairway.
McDowell was looking very tight by now, and dragged his ironed approach to the left and into the greenside bunker. McIlroy produced a moment of sheer brilliance to flop the shot to within five feet.
Snedeker had whipped a low shot safely onto the green, leaving Furyk around 20 foot. He couldn't hole it, meaning that McDowell had a putt for a point.
He managed to keep his nerve once more to limp over the line for Jose Maria Olazabal's charges.