Rose, the 2013 US Open champion from England, and Sweden's Stenson combined to beat Bubba Watson and Webb Simpson 5 and 4 in morning fourballs and Hunter Mahan and Zach Johnson 2 and 1 in afternoon foursomes at a cool and windy Gleneagles.
"The wind was gusting and you could sort of lose your confidence very quickly out here. When the wind is buffeting you, very easy to miss putts," Rose said. "It was nice to kick on this afternoon and get that point."
Europe's biggest fightback was by McIlroy and Garcia, who lost 1-up to Mickelson and Bradley in fourballs but halved with Fowler and Walker.
"We needed it, we really did," McIlroy said. "It was big and at least we get something out of the day. We played two really tough matches and we have half a point to show for it."
McIlroy sank a 40-foot birdie putt at the par-3 17th hole to send the match to the par-5 18th, where Garcia dropped his 5-wood approach 25 feet from the hole. McIlroy missed his hard-breaking eagle putt but the tap-in birdie was enough to win the hole and swipe a half-point.
"We fought as hard as we could," Garcia said. "Half a point is just huge."
And an early US lead had vanished.
"It's amazing how different a feel it is from the morning to the afternoon," Walker said. "Exciting, exhilarating, heartbreaking, excruciating. You get it all. It was really fun."
Europe, seeking a sixth win in seven tries, need 14 points to keep the trophy while the Americans need 14.5 to reclaim the Cup. Fourballs and foursomes will be played again on Sunday (NZT) followed by 12 concluding singles matches on Monday (NZT).
McDowell and Dubuisson, who sat out the morning session, beat five-time major winner Mickelson and Bradley 3 and 2 as the 24-year-old rookie sparkled.
"This kid is the next superstar in Europe," McDowell said. "He didn't need much advice. Just wind him up and let him go."
Dubuisson, Europe's youngest player, shook off his anxiety quickly.
"I was a little nervous," he said. "When I got on the tee with Graeme it was just a dream. It was fantastic. My stress completely disappeared."
McDowell, who clinched the victory with a 15-foot birdie putt at the 15th, was not the only winning mentor to a newcomer in foursomes as England's Lee Westwood and Welsh rookie Jamie Donaldson beat Jim Furyk and Matt Kuchar 2-up.
Westwood, a captain's pick ranked lowest in the Cup field at 44th, moved to 5-0 with two halved in Cup pairs matches against fourth-ranked Furyk, each making his ninth Cup appearance.
"There was no doubt in my mind Jamie was up to the task," Westwood said. "We played well out there, about 4-under, and that's a quality match under these conditions."
In the morning, Mickelson birdied the 18th hole for a 1-up victory alongside Bradley over Garcia and McIlroy, but it was Ryder Cup newcomers who sparked the Americans to an early surge.
US rookies Jordan Spieth and Patrick Reed routed Scotsman Stephen Gallacher and England's 2012 Ryder Cup star Ian Poulter 5 and 4, dimming the impact of Rose and Stenson's first win.
Walker, making his Cup debut at 35, blasted out of a bunker for an eagle at the ninth, chipped in from the rough for a birdie at 16 and sank the match-halving six-foot birdie putt at 18 to swipe half a point from Martin Kaymer and Thomas Bjorn, who led from the first hole until the final shot.
-AAP
