The home team went ahead at the first hole, as McIlroy could only find the bunker with his approach.
Despite playing a good up and down, Johnson rolled in for his birdie having dialled in a wedge to the green.
Poulter missed a putt from just a couple of feet at the next green, meaning that the Americans went two up.
He atoned for that error at the fourth by holing a tricky putt to claw a hole back.
However, the Americans were able to restore their two-up advantage before the players reached the back nine.
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