Asia were on course to win the title for the first time at the third attempt as they held a slender 6.5-5.5 lead after Saturday's play.
But Europe won seven of the first eight singles games on Sunday to take a commanding lead, while Asia did respond with three wins and the final match finished all-square.
Alex Noren, Rafa Cabrera Bello, Tommy Fleetwood, Tyrrell Hatton, Henrik Stenson, Bernd Wiesberger and Alexander Levy were all winners before Belgium's Thomas Pieters, who impressed on his Ryder Cup debut at Hazeltine in 2016, secured the winning point.
Captain Thomas Bjorn, who will have been impressed with several players ahead of the Ryder Cup clash against the United States at Le Golf National in Paris in late September, said on the European tour website: "I'm very proud of them - a great team, great morale.
"They knew they had to keep going until the end, they knew they were up against something - there was a special atmosphere in that Asian team - and they knew they had to work hard.
"Today, I can only say that every single one of them stood up and did everything they could and I'm just very proud of these boys.
"They worked so hard this week and they worked well together.
"As a group we've had a really good time. We wanted to win, we didn't want to travel this far at this time of the year not to win.
"We wanted to come out here and show that European golf is more than 12 strong, we are all the way through.
"A lot of these guys deserved their points today, they worked hard this week and might not have got too much out of it, and today they did."