Europe beat the US in the closing 12 singles to complete a second straight 18.5 to 9.5 points rout.
The victory marked the first time that the Europeans had won three times in a row, and consigned the US to fifth defeats in the last six Ryder Cup tournaments.
Sweden's Henrik Stenson sank the winning putt, defeating JJ Taylor four and three on the 15th green.
Ulsterman Darren Clarke then won his singles against Zach Johnson on the 16th green, to round off a comprehensive victory for the Europeans.
European won all five sessions for the first time and took the concluding 12 singles by 8.5 points to 3.5, their biggest ever winning margin.
"I just can't say enough about my team," said Ian Woosnam, European captain.
"I just can't say enough about my team"
- Ian Woosnam, European captain
"They have played fantastic," he said. "I was on edge for a little bit but as that blue got more and more on the board I got more comfortable."
"I can now hand it on to (Nick) Faldo and he can try to make it four in a row," he added. Faldo has already been named as Europe's Ryder Cup captain for the next meeting in two years time.
Tom Lehman, US captain, saluted the European team.
"I tip my hat to them. Our team came very ready but I guess we weren't quite ready enough," he said.
"I need to give credit where credit is due and the European team played better."
Woosnam's twelve men went into the final day with a commanding 10-6 lead after four hard-fought sessions of fourballs and foursomes on Friday and Saturday.
An American comeback did not materialize, and the leaderboards were soon dominated by the blue of Europe.
Europe's main defeat on Sunday came from Sergio Garcia, who quickly fell four down to US wildcard Stewart Cink.
No way back
There was no way back for the 26-year-old Spaniard but he had been the star turn on the first two days winning all four of his games.
Cink apart, the only other American who bucked the trend early on was Tiger Woods, world number one.
"I need to give credit where credit is due and the European team played better"
- Tom Lehman, US captain
Woods edged ahead early on giant Swede Robert Karlsson and he finished it off three and two at the 16th to bring his Ryder Cup record in singles to won three, lost one and halved one.
But by that time Montgomerie had already come in with Europe's first point, sinking a six-footer on the 18th against Toms to win by one hole. Montgomerie joins an elite group of players on six Ryder Cup singles wins.
Englishman Paul Casey soon followed, finishing off Jim Furyk two and one and inflicting a first defeat in five singles matches on the world No.3.
David Howell crushed Brett Wetterich five and four to make it 13-8 and then two wins seconds apart from Luke Donald two and one over Chad Campbell and finally Stenson clinched the Ryder Cup for Europe.
"I didn't know that was the one, but I'm delighted to win my match," rookie Stenson said.
Minutes later came Darren Clarke's emotional win.
"This is just as good as it gets and for the Irish it's just fantastic," he said.