Koepka, a double major victor this year, fared much better for the Ryder Cup holders as he found the short grass from the tee and hit a solid approach to eight feet, although his birdie putt shaved the right edge of the hole.
The American golfer, 28, struck the supporter in the face on the short, par-four sixth hole attempting a monster drive. Sergio Garcia and Alex Noren blew out Phil Mickelson and Bryson DeChambeau 5 and 4.
At the turn, USA duos led in three matches with Europe atop the other.
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After a morning session in which the United States rolled to a 3-1 lead, Europe came storming back in the afternoon foursome sessions.
Fleetwood, one of four Europeans making their Ryder Cup debuts, kept it from being another shutout by teaming with British Open champion Molinari for a 3-and-1 victory over Woods and Patrick Reed. The U.S. never led in the match until it won. He followed with a 35-foot birdie putt, crouching to watch as it broke into the cup.
Watson and Simpson birdied the par-3 11th thanks to Watson's pinpoint accuracy on his tee shot but McIlroy and Poulter won the 12th, 13th and 16th holes to win the match 4 and 2.
In a ideal world both Mickelson-DeChambeau and Simpson-Watson - who are 0-2-0 in foursomes play when teamed together compared to 2-0-0 as a fourball team - would have been better served in the morning format, but then that wasn't the plan. Logically, Finau and Koepka will be paired together again Saturday morning, and then all 12 players from each side will compete in Sunday's singles matches. Rose found the water on his second shot; Rahm missed the green with his approach and his 20-foot par putt failed to drop.