However, Nick Kyrgios and Jack Sock then handed Team World their first point by beating Rafael Nadal and Tomas Berdych in the day's closing doubles rubber to reduce the deficit to 3-1.
Europe were Sky Bet's 1/4 favourites before a ball was struck and they look well on course to reach the victory target of 13 points over the next two days of competition.
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Marin Cilic and Dominic Thiem had defeated Frances Tiafoe and John Isner, respectively, to hand the Europeans an early lead at the three-day tournament in Prague.
Austrian Thiem outlasted American Isner in a champions' tie-break - a first-to-10-points race used to settle matches that are tied at one set apiece.
After 12 games went with serve, before Isner's backhand caused a mini-break point during the first set tie-break which he eventually won 17-15.
A tie-break was also needed to settle the second set but Thiem romped five points clear before forcing a decider which he won.
Earlier, Cilic of Team Europe secured a 7-6 7-6 win over Tiafoe of Team World.
Cilic, a former major champion and the world No 5, had a vast experience advantage over the 19-year-old Tiafoe and pipped a tie-break in the second set to seal victory.
Cilic's eventual win looked likely after taking the first set but Tiafoe, the American currently ranked 72nd in the world, led much of the second set before finally conceding the impetus.
In a clash of the teams' youngest players, Germany's 20-year-old world No 4 Alexander Zverev overpowered Canada's 18-year-old Denis Shapovalov 7-6 7-6 in another rubber without breaks.
Kyrgios and Sock then upset US open champion Nadal and Berdych in the day's closing doubles rubber, winning 6-3 6-7 (7/9) 10-7.
Czech Berdych lost his serve halfway through the first set as off-court friends Kyrgios and Sock seemed far more comfortable on the black court of Prague's O2 Arena.
Berdych and Nadal regained some momentum in the second set, but the Team World duo grabbed the super tie-break.
Skippering Team Europe, Bjorn Borg decided to rest world No 2 Roger Federer on the opening day while John McEnroe decided not to use his highest-ranked player, world No 16 American compatriot Sam Querrey.
With two points for each win on Saturday - rather than one on the opening day - both look set to play a part on the second day of action.
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