The Englishman and the Swede were in action for a second time, having defeated Bubba Wtason and Webb Simpson 5 and 4 in the morning fourballs.
Wildcard Mahan and former Masters champion Johnson were out for the first time, having been rested by skipper Tom Watson for the fourballs. They played both foursomes two years ago at Medinah, winning one and losing one.
“Its been really, really special for us today,” Rose said. “I thought we were really good all day today and it was just a great day — really enjoyed it.”
Rose, who had been in superb form in the morning, was the driving force again as he and Stenson nabbed birdies at the first and sixth to ease two ahead.
Mahan and Johnson, however, pegged that back to one at the next and they were level a hole later when Rose missed a two-footer for a halve.
It stayed that way through the turn with Johnson missing an eagle putt at the ninth that would have nudged the Americans ahead.
Europe were ahead once more thanks to a big Rose birdie putt at the 11th and after answered after a US birdie at 14 with a victory at the 15th when the Americans made bogey.
Two holes later, Rose clinched a second point for himself and Stenson when he holed a two-footer for par and the victory.