Trailing 3 1/2-2 1/2 after Friday's fourballs, Thomas Bjorn's side quickly erased the deficit and then moved ahead by winning three of the first four matches at the Glenmarie Golf and Country Club.
However, the Arjun Atwal-captained Asia team, finished with a flourish by picking up the remaining three points to end the day 6 1/2-5 1/2 ahead, retaining their hopes of winning a first EurAsia Cup title at the third edition of the event.
In the 2016 competition, Darren Clarke's European team romped to an 18 1/2-5 1/2 blowout victory over their Asian counterparts after the inaugural matchplay contest was tied two years earlier.
Race to Dubai winner Tommy Fleetwood and Henrik Stenson put Europe on the board as they tied the overall score on Saturday by handing the visitors a 3 and 2 win over Indian pairing Anirban Lahiri and S.S.P Chawrasia.
"It was a really good morning, we played really solid. We didn't make a bogey, we made quite a few birdies and in foursomes that's going to be hard to beat, really," Englishman Fleetwood said after the match.
"I won't mind playing doubles again, I have really enjoyed playing this team game... Looking forward to the singles and we will see where we are at the end of the day."
Britons Paul Casey and Tyrrell Hatton then picked up a 2 and 1 win against An Byeong-un of South Korea and Thailand's Kiradech Aphibarnrat as Europe moved ahead.
Matthew Fitzpatrick and Thomas Pieters then gave Europe a two point-lead with a 3 and 2 win against Kang Sung-hoon and Poom Saksansin in the fourth match of the day.
Asia needed something special to stop the rot and the Japanese-Malaysian pairing of Yuta Ikeda and Gavin Green stepped up to the plate by winning three of the last four holes for a rousing 1-up win over Alex Levy and Rafa Cabrera.
Thai teen Phachara Khongwatmai and Hideto Tanihara levelled the score with a 2 and 1 win over Paul Dunne and Alex Noren, before Li Haotong and Nicholas Fung put Asia back in front with a 3 and 1 victory against Bernd Wiesberger and Ross Fisher.
(Reporting by Sudipto Ganguly in Mumbai; Editing by John O'Brien)
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