The fan lay on the ground after American golfer Brooks Koepka's opening shot at the sixth hole of the tournament veered off target and struck her just above the eye.
American captain Jim Furyk opted to deploy two of the three winning duos from the morning session-Johnson and Fowler, and Thomas and Spieth-in the afternoon while subbing out the Brooks Koepka and Tony Finau, the team that came back to beat Justin Rose and Jon Rahm in the morning session.
"We were in control of the match being 2-up, but we just didn't make any birdies coming in", Woods said.
But Molinari made consecutive birdies at the 11th and 12th holes to square the match, and neither Woods nor Reed could make a birdie the rest of the way. The U.S. never led in the match until it won.
More than 7,000 spectators at Le Golf National jammed into the largest first-tee grandstand in Ryder Cup history, cheering and screaming to produce a roar unique to the emotional atmosphere of the biennial team golf showdown.
Fabregas warns Chelsea about Hazard exit next summer
I play in strong teams, here with Chelsea and with Belgium who were very good at the World Cup, and that helps me to perform better too".
Asked if he would work on any aspect of his game ahead of Day 2, Woods, whose Ryder Cup win-loss-halve record now reads 13-18-3, replied: "I'm not going to work on anything". Paul Casey rallied with three straight birdies to square the match before Thomas delivered a key shot over the water to six feet on the 15th for a birdie. Molinari closed it out with a birdie on the 17th. Tyrrell Hatton missed a 20-foot birdie attempt on the 18th, and Spieth rolled in his 3-foot par putt for a 1-up victory. They haven't led after an opening session since 2006.
Dustin Johnson and Rickie Fowler had the easiest match of the morning, thanks in part to a flat performance by Rory McIlroy, who didn't contribute a single birdie playing alongside Danish rookie Thorbjorn Olesen.
The pairing lost seven of the first nine holes and looked out of sorts after Mickelson found the water while laying up with an iron off the par-5 3rd tee.
Johnson and Fowler gave the U.S. its first point, closing out the 4-and-2 victory over McIlroy and Olesen without even having to finish the par-3 16th.