Despite arriving at the course late, the Northern Irishman made a solid start. He went ahead at the fourth when Bradley veered off course with his approach.
Bradley sank a tough 15-foot putt to deny McIlroy another hole at the fifth.
However, he could do nothing to prevent the 23-year-old from extending his lead at the next hole, as McIlroy chipped in to the delight of the European fans.
A birdie at the 10th and a par at the 12th saw Bradley haul McIlroy back to all square and the game was back on, with the resurgent American crowd backing their man all the way.
McIlroy showed some strength just when he needed to, carding birdies at 14 and 15 to once again move into a two-hole lead.
The next two holes were halved, which was enough for Europe to level the overall scores at 10-10.