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After the opening three holes were shared, Garcia drew first blood for the home side by holing from the greenside bunker at the fourth, but the Spaniard missed a short putt on the seventh to allow USA to level the game.
A moment of brilliance from the bunker from Mickelson saw the American pairing edge ahead at the turn, and they extended that lead after Bradley holed out from distance on the 10th.
However, both Mickelson and Bradley made bogeys on the next hole to allow Europe to halve the deficit before they levelled the game with five to play.
In what was turning out to be a see-saw affair, McIlroy and Garcia edged ahead when Mickelson missed a short putt, but Bradley hit straight back for the Americans with an eagle on the par-five 16th.
The game went to the last hole with all four players failing to hit the green, but it was Bradley and Mickelson who made the best effort with their recovery shots to leave Mickelson with a three-foot putt to steal the point from Europe.
USA's win has given them a 2.5-1.5 lead over Europe after the first four matches.