The defending champions had a commanding five-point lead heading into the final day. But Continental Europe won Sunday's first five singles to level the contest with each team on 11½ points.
It took narrow wins by Ian Poulter, Scott Jamieson and Mark Foster to clinch victory.
"Losing five and a half points out of the first six was a big body blow to the team," Britain & Ireland captain Paul McGinley told the European Tour website. "But fortunately the guys at the end came through when I really needed them."
Continental Europe captured the inaugural event in 2000, but Britain & Ireland have since won the trophy six straight times.
Thomas Bjorn beat Lee Westwood 2 and 1 to earn the first point and spur Continental Europe's comeback. The European Masters winner made four birdies and capitalized on three bogeys from Westwood to rally from 3 down.
"Lee came out this morning and was sensational the first few holes," Bjorn said. "It was just a case of hanging on and hanging on, but a couple of mistakes and it let me back in. I played some nice stuff near the end, but it was a hard-fought battle."
Francesco Molinari outplayed Jamie Donaldson 4 and 3. The Italian had a bogey-free day, sinking three birdies to add a second point for Continental Europe.
Alexander Noren cruised to a 4 and 3 win over Robert Rock. The Swede was 5 up at the turn and protected his lead on the back nine despite two bogeys.
Miguel Angel Jimenez defeated Darren Clarke 4 and 2 to tie the contest at 11½-11½. The Spanish veteran made the difference by winning four holes on the back nine as the match was still all square at the turn. British Open winner Clarke performed poorly, making five bogeys and a double.
Nicolas Colsaerts trailed by two but the Belgian birdied the 15th and holed an eagle on the 17th to halve his match with David Horsey.
Jamieson beat Pablo Larrazabal by a hole to give Britain & Ireland a 13-12 lead. Larrazabal had 3 bogeys and a double bogey to go 4 down after 10 holes and could not fully recover despite 3 birdies and an eagle on the back nine.
"We knew they were going to come out hard and fast," Jamieson said. "They certainly got the momentum going. I saw on the 15th green the first five matches and that we had lost them all."
"I knew my point was probably going to count and be a deciding one. I was proud that I hung in there and made it count."
Poulter edged Matteo Manassero by a hole. The Italian teenager led until the 15th but Poulter birdied the last three holes to fire Britain and Ireland to a 14-12 lead.
"Matteo played very solid today," Poulter told Canal Plus television. "He made me have to win my match. I was aggressive in the last few holes and it paid off."
The World Match Play champion was the best player for Britain & Ireland, earning four out of five points.
"What a man to have on a team," McGinley said about Poulter. "It's not just the way he plays golf and his love of match play, but his personality is infectious around the place. Absolutely infectious."
"I would have him in the team every day of the week. No doubt about that. And I think the Americans would too if they could."
Foster birdied the 17th and parred the 18th to beat Raphael Jacquelin by a hole and secure victory for Britain & Ireland.
All the players on the Continental Europe team were in the world top 100, while Britain & Ireland had three players ranked outside the top 100 — Foster, Rock, and Jamieson.
"I'm kind of relieved," McGinley said. "We were underdogs, then we became strong favorites going into the singles and we just about got over the line."