The USA remain without a win on European soil since 1993 while neither team have lifted the trophy away from home in 11 years.
With Europe needing half a point to get over the line, Fleetwood moved 2-up against Rickie Fowler with two holes to play after the American dumped his tee shot on the short par-four 16th into the water.
Fleetwood struck his drive into the heart of the green and calmy stroked his eagle putt to the holeside to ensure Europe a seventh consecutive home victory, before going on to win 3 and 1. "I think relief, pride, joy," said the Englishman. "Proud of everybody that's been involved this week and just proud that I'm one of the people that gets to play a role in what we came here to do." US captain Zach Johnson took responsibility for the loss. "The defeat is on me, I made some poor decisions and I will reflect.
Those 12 guys played so hard and fought for our country," he said. Rory McIlroy and Viktor Hovland led the way with early victories in the Rome sunshine and Jon Rahm also snatched half a point from Scottie Scheffler on the 18th green.