European captain Miguel Angel Jimenez and fellow Spaniard Pablo Larrazabal gave them the perfect start by beating Team Asia leader Thongchai Jaidee and Kiradech Aphibarnrat 2 and 1 in Malaysia's capital Kuala Lumpur.
Three of the other five matches were as easily won by the Europeans at the Glenmarie Golf and Country Club.
Only Malaysia's Nicholas Fung and his South Korean partner Kim Hyung-Sung had a good opportunity to give Asia a point after going three-up through seven holes.
But Europe's pairing of Graeme McDowell and Jamie Donaldson went on the offensive and turned it around to register a 3 and 1 victory.
"We somehow managed to make the turn at one-down which was huge," McDowell said. "And this guy (Donaldson) had a phenomenal back nine... It was great to watch."
Danish pairing Thomas Bjorn and Thorbjorn Olesen beat Japan's Koumei Oda and Hideto Tanihara 2 up while France's Victor Dubuisson and Joost Luiten of the Netherlands defeated Thai Prayad Marksaeng and Bangladesh's Siddikur Rahman 3 and 2.
Spain's Gonzalo Fernandez-Castano and Stephen Gallacher of Scotland enjoyed the biggest win of the day, defeating India's Gaganjeet Bhullar and Anirban Lahiri 4 and 3.
Before tee-off, Malaysia's prime minister led a minute of silence together with the two team captains as a tribute to Malaysia Airlines flight MH370.
Malaysia says the Beijing-bound flight that lost contact shortly after take-off from Kuala Lumpur on March 8 crashed into the southern Indian Ocean with 239 people aboard.
All players and officials wore black ribbons, and visitors were able to leave a message on a wall of condolence, the organisers said.
The new Ryder Cup-style team tournament has incensed the administrators of a rival tournament, the Royal Trophy, a similar Europe versus Asia competition launched in 2006.
Organisers of the Royal Trophy, which was spearheaded by late Spanish great Seve Ballesteros, have repeatedly cried foul over the EurAsia Cup and sparred with the European Tour, a joint backer along with the Asian Tour.
"In our opinion, today is a very sad day for golf," Ivan Ballesteros, co-managing director of the Royal Trophy and nephew of Seve, said Thursday.
"For us, the launch of the EurAsia Cup is an act of aggression by the Asian and European Tours against the Royal Trophy and all of its partners," he added in the statement.
The EurAsia Cup continues with five foursomes pairings on Friday and finishes with 10 singles matches on Saturday.
Europe only need another five-and-a-half points from the 15 that will be available over the next two days to claim the trophy.
Thongchai, who has been bullish about his team's chances, said he was still hopeful of better days ahead.
"We will make changes to our partnership for tomorrow... as it is a tricky format," the Thai said.
"We have to be at our best if we are to close the gap. The Europeans have more experience playing in this situation."
Donaldson too said he was not underestimating Asia despite the first round whitewash.
"To be five-nil up is a fantastic start. We have always said we can't underestimate them, because at the end of the day, we are playing in Malaysia," the Welshman said.
Miguel Angel Jimenez and Pablo Larrazabal (Europe) beat Thongchai Jaidee and Kiradech Aphibarnrat (Asia) 2 &1
Graeme McDowell and Jamie Donaldson (Europe) beat Nicholas Fung and Kim Hyung-Sung (Asia) 3&1
Thomas Bjorn and Thorbjorn Olesen (Europe) beat Koumei Oda and Hideto Tanihara (Asia) by 2 holes
Victor Dubuisson and Joost Luiten (Europe) beat Prayad Marksaeng and Siddikur Rahman (Asia) 3 & 2
Gonzalo Fernandez-Castano and Stephen Gallacher (Europe) beat Gaganjeet Bhullar and Anirban Lahiri (Asia) 4&3