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McIlroy and Garcia capitalised on two bogeys from their opponents to win the first two holes, but the Americans responded on the next to halve the deficit.
Neither team was prepared to give an inch as they made it five successive holes that had been shared, but Europe had the advantage at the ninth after making the green in two.
The European duo did enough for a four, but Furyk holed from 25 feet to ensure that his team didn't fall further behind to the world number one and three.
You can keep track of the back nine by following Sports Mole's live text commentary.