The victory handed Cilic's Europe side the first point of the competition which has been organised in homage to Australian tennis legend Rod Laver.
Billed as the tennis version of golf's Ryder Cup, the competition pits Europe's best players against six from the rest of the world.
Roger Federer and Rafael Nadal, winners of 35 Grand Slam events between them, are the star names in the European line-up skippered by Bjorn Borg.
The Rest of the World team does not boast that calibre of firepower. The only person in their roster to have tasted major success is team captain John McEnroe.
"Bjorn defintely wants to win," said Federer. "And John does not want to lose even though we are the big favourites."
Winners of the four matches on Friday each gain a point and on Saturday they are rewarded with two points. It is three points for a victory on Sunday's final day. The first team to 13 will hoist the trophy.
"They should be more than exhibition matches," said Federer. "I know that some people have mentioned the word 'exhibition' but I don't like it and it shouldn't be the case because we are playing in honour and for the legacy of Rod Laver."