Click here for the final scorecard.
Speaking after his win, which secured the trophy for Europe, Fleetwood told Sky Sports: "I didn't want it to come down to one of us at the back.
"I can't wait to see the rest of the guys, the captain, the vice-captains, our wives, our families and the staff. I'm so happy to play a part in it.
"I'm so proud, we have an amazing group of people. This year has been very different and the landscape has changed for Europe, but I couldn't wish for a better bunch of people to do with this.
"We are one gigantic family and the bonds you make last a lifetime. This is just so cool."
With just four points needed from 12 singles to win, Europe had to wait until Fleetwood came through in the 11th match as they took an unassailable 15-11 lead.
Bob MacIntyre added a 16th point afterward and Shane Lowry then wrapped it up at 16.5-11.5.
Rory McIlroy and Viktor Hovland led the way with early victories in Rome and Jon Rahm also snatched a half-point from Scottie Scheffler on the 18th green.
Luke Donald's Europe started the day four points from lifting the trophy they lost in a record-breaking 19-9 thrashing at Whistling Straits two years ago.
They raced out of the blocks in the Rome sunshine before the USA enjoyed a surge to quieten the huge home crowds, at one point leading in seven matches and tied in the other.
The Americans were attempting to pull off the biggest Sunday Ryder Cup comeback, having trailed 10.5-5.5 at the start of the day, and win on European soil for the first time since 1993.
Still only four teams have come from behind on Sunday to win the trophy since continental Europe joined the event in 1979, with the Americans' 1999 'Battle of Brookline' success and Europe's 'Miracle at Medinah' coming from having been 10-6 behind.
Europe's big guns fire
Rahm grabbed a crucial half-point from a thrilling opening tussle with Scheffler by making birdie on the par-five 18th hole after the world number one thinned a chip across the green.
"We've had a couple of really good matches. He's a heck of a competitor," said Rahm. "You know, my hat's off to him and I'm glad I could get a half."
Viktor Hovland had already romped to a 4&3 victory over Collin Morikawa to take his personal tally for the event to 3.5 points - the same as Rahm.
Patrick Cantlay, the pantomime villain after reports he was refusing to wearing a hat over wanting to be paid at the event before his caddie Joe LaCava angered McIlroy on Saturday, edged out Justin Rose 2&1.
McIlroy, who ends the week with four points, closed out a 3&1 win over Sam Burns despite a late rally from the American.
Tyrrell Hatton overcame some nervy late moments to see off British Open champion Brian Harman on the 16th hole and put Europe on the cusp and 14-7 ahead.
Matthew Fitzpatrick missed a 19-foot birdie putt to win the Ryder Cup on the last hole as Max Homa kept the fate of the matchplay showdown just about in the balance.
Homa, who was the USA's best player at Marco Simone Golf and Country Club with 3.5 points, bravely opted to take a penalty drop from the rough for an unplayable lie, but made a clutch up and down for par.
Brooks Koepka saw off Swedish sensation Ludvig Aberg 3&2 and Xander Schauffele beat Nicolai Hojgaard by the same scoreline.
