Trailing by a point heading into the singles, Nick Faldo's team won six and halved two of the first eight matches to clinch the victory with two singles left.
Bradley Dredge got the decisive win by making a birdie to go 2 up with two to play against Gonzalo Fernandez-Castano.
Colin Montgomerie, who lost all three of his earlier matches for Britain and Ireland in the tournament, won the opening singles 1 up against Robert Karlsson.
Europe's only win came from Peter Hanson, who beat Oliver Wilson 1 up.
'The guys all came through,' Faldo said. 'They showed great determination to win. They all did their bit.'
Faldo will captain Europe's Ryder Cup team that will defend its title in Kentucky next year.
Paul Casey rediscovered his form to beat Raphael Jacquelin 3 and 2 in the second match after making seven birdies in the first 11 holes. Marc Warren, who also struggled earlier in the week, beat Gregory Havret 1 up in the third match.
The winners said they were buoyed by a television prediction Saturday that they would all lose their matches.
'That was a nice bit of motivation right there,' Casey said.
Britain and Ireland' s biggest victory Sunday came from Graeme Storm, 6 and 5 over Thomas Bjorn. Storm had five birdies without dropping a shot through 13 holes against Bjorn, who was recovering from an upset stomach.
Simon Dyson, one of Faldo's wild card picks, shot five birdies in 11 holes to rally for a 2-and-1 victory over Mikko Ilonen.
'I loved it all week. We've carried each other along and it's just got better all week,' Dyson said.
Bradley Dredge, the week's top scorer with 4 points out of five, beat Gonzalo Fernandez-Castano 2 up with a birdie at the last.
Justin Rose held off Miguel Angel Jimenez 2 and 1 after being five ahead through 11 holes.
'Everything went wrong. I looked at the draw this morning and thought it was perfect,' said Europe captain Seve Ballesteros, for whom the tournament is named. 'Britain and Ireland played great golf.'
Britain and Ireland has now won the event four of the five times it has been played.
The event is scheduled to return to The Heritage here in 2009.