Left-hander Watson and Cup rookie Simpson beat England's Justin Rose and Italian Francesco Molinari 5&4 to give the home team a commanding 9-4 lead over holders Europe in front of energized crowds at Medinah Country Club.
Watson sealed the win with a two-putt birdie at the par-five 14th, but U.S. Open champion Simpson paved the way to victory with a red-hot putting display as he piled up seven birdies on his own ball.
Bidding to win the Ryder Cup for only the second time in the last six editions, the Americans need a total of 14-1/2 points to regain the trophy and they led in two of the other fourball matches with the Europeans ahead in one.
Dustin Johnson and Matt Kuchar were one up on Nicolas Colsaerts and Scot Paul Lawrie after 13 holes while Jason Dufner and Zach Johnson were two up on Northern Ireland's Rory McIlroy and Englishman Ian Poulter after 11.
Spaniard Sergio Garcia and Englishman Luke Donald provided Europe's lone source of inspiration in dazzling afternoon sunshine, going two up on struggling Americans Woods and Steve Stricker after 12 holes.
The U.S. duo had been benched for the morning session after losing their first two matches at Medinah but they did not benefit from the rest as they mustered just one birdie between them over the front nine.
U.S. captain Davis Love III had set up the course with virtually no rough and slick greens. While delighted his team have mainly taken full advantage over the first three sessions, he cautioned them not to get complacent.
"What I keep telling these guys is we're not even halfway over with this tournament so far," Love said. "There's a lot of points left, let's keep doing what we're doing.
"They're buying into it. They're playing great. They like what's happening so far, and they're just going out there and playing golf."
Europe's position was looking increasingly grim, especially given that the biggest comeback going into the last-day singles came at Brookline in 1999 when the U.S. triumphed after trailing 10-6.
"Our boys are not making the putts," Europe captain Jose Maria Olazabal said. "Some of them haven't performed to their expectations."
The Americans had piled the pressure on the Europeans after winning three of the four foursomes matches in the morning to stretch their overall lead to 8-4.
Phil Mickelson and Keegan Bradley set the tone, crushing out-of-form Englishmen Lee Westwood and Luke Donald 7&6, their third triumph together this week equaling the biggest victory margin in Ryder Cup team play.
Americans Hale Irwin and Tom Kite beat Ken Brown and Des Smyth 7&6 at the 1979 Ryder Cup, and compatriots Paul Azinger and Mark O'Meara followed suit against Nick Faldo and David Gilford in 1991. (Editing by Julian Linden)