Berdych and world No 1 beaten in doubles on Day 1, but teammates Cilic, Thiem and Zverev got them off to a good start.
Nadal happy after Team Europe take lead over Team World Cup at Laver Cup
Marin Cilic, Dominic Thiem and Alexander Zverev won their opening singles to put Team Europe ahead of Team World after Day 1 of the inaugural Laver Cup in Prague on Friday.
Nick Kyrgios and Jack Sock then handed Team World their first point by beating Tomas Berdych and world No 1 Rafael Nadal in the day's closing doubles rubber to round off the score at 3-1 for Europe.
"I'm happy the way the day went, we had a couple of wins that were super close and we could lose," Roland Garros and US Open champion Nadal said.
"We have a good result for our team. Happy to go to back to bed with 3-1 and tomorrow is another day."
With four matches a day - three singles and a doubles, the players can earn a point for each win on Friday, two on Saturday and three on Sunday.
World No 5 Cilic beat 72nd-ranked Frances Tiafoe, a replacement for the injured Argentine Juan Martin del Potro, 7-6, 7-6 in the tournament opener.
The big-serving Croat and the 19-year-old American held on to their serves in the first set before earning a break apiece in the second, with Cilic showing better nerves in both tie-breakers.
Seventh-ranked Austrian Thiem then put Europe 2-0 ahead, beating world No 17 John Isner 6-7, 7-6, 10-8.
Shot of the day
Isner offered his regular dose of aces as both held on to their serves throughout the rubber, taking it to the 10-point super tie-break used to decide games tied after two sets.
Isner went 4-0 up in the super tie-break, but the patient Austrian came back to win the rubber.
In a clash of the teams' youngest players, the 20-year-old world No 4, Zverev, overpowered 18-year-old Canadian Denis Shapovalov 7-6, 7-6 in another rubber without breaks.
In the doubles, 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.
Leading Team Europe, Bjorn Borg decided to rest world No 2 Roger Federer on Friday while John McEnroe decided not to use his highest-ranked player, 16th-ranked Sam Querrey.