Rose holed his 15-foot birdie putt at the last for a superb 67 of his own, punching the air in delight before warmly embracing the American who now adds his second major to his Olympic gold medal.
Horschel then followed suit, making birdies on the last three holes for a 68 to join Rose, while South African Thriston Lawrence finished fourth on six under after another three-under round.
The Australian challenge had earlier petered out when Adam Scott finished with a level-par 71 to finish tied for 10th, also at even par overall, while Jason Day shot a 68 to end up in joint-13th spot.
