By Mitch Phillips

ROME (Reuters) -Europe have another home Ryder Cup victory tantalisingly within their grasp after ending Saturday five points ahead but the United States earned a glimmer of hope by taking the fourballs 3-1 in a high-octane finale as the sun set on the 18th hole.

Patrick Cantlay ended a controversial personal day by birdying the last three holes, winning the last two, to snatch win the final fourball and flip the session in America's favour.

However, after another scorching Rome day, Europe still led 10-1/2-5-1/2 and need four points from Sunday's 12 singles to regain the trophy and continue their incredible 30-year unbeaten home run in the biennial competition.

They began the day as they finished on Friday -- in control.

Inspired by a Ryder Cup record 9&7 victory for Viktor Hovland and Ludvig Aberg, Europe took the morning foursomes 3-1 using the same four pairings who swept a 4-0 success on Friday.

Trailing by seven, the shellshocked U.S. team knew if they were to have any hope of a miracle comeback they would have to make inroads in the afternoon.

They made a good start as Sam Burns and Collin Morikawa brought Hovland and Aberg down to earth with a 4&3 win, before the impressive Max Homa and Brian Harman beat Tommy Fleetwood and Nicolai Hojgaard 2&1 to close the gap to five.

All attention then turned to the two tight remaining matches, with fans packing round to watch the closing holes fully aware of the importance of their outcome.

Justin Thomas and Jordan Spieth led early on against Justin Rose and Bob MacIntyre but the British duo played a brilliant back nine to triumph 3&2, having won their last two holes to snatch half a point in their first fourball on Friday.

The final match was a fantastic battle between Rory McIlroy and Matt Fitzpatrick and Cantlay and Wyndham Clark.

They halved 11 of the first 13 holes before McIlroy, who had won his first three matches, brilliantly birdied the 14th to gain the edge.

Cantlay kept the match alive on 16 then hit a great birdie two on 17 to make it the first match of the day to go down to the 18th -- where Cantlay drilled a 20-foot putt for a precious point.

He had been the butt of the home crowd’s humour all afternoon after a media report said he was refusing to wear his team cap in protest at players not being paid to play in the Ryder Cup.

In response, his team mates took off their caps and swirled them in the air at the suddenly silent crowd crammed around the 18th -- a gesture not appreciated by the two European players still waiting to putt. McIlroy was later seen angrily remonstrating with some the of U.S. team and said it all "added fuel to the fire" for Sunday.

Cantlay, who later claimed his decision was purely because he could not find a comfortable hat and dismissed talk of a protest, said: “The crowd was on me all day, I just used it as fuel. Hopefully we can build a lot off this small amount of momentum we’ve got going.

"I told Wyndham we’re going to use it all day. I have never had so many standing ovations walking from tee to green.

"We’ve seen what they did at Medinah, and we have a steeper hill to climb but we’re going to give it our best shot.”

The biggest Ryder Cup comeback was 2012’s “Miracle of Medinah” when Europe trailed 10-4 with two Saturday matches still on the course. They won them both to start Sunday 10-6 down then won eight and halved one of the 12 singles to triumph by a point.

(Reporting by Mitch Phillips; Editing by Ed Osmond and Clare Fallon)