But Real did not wait long to make Berg pay, as Karim Benzema teed up Modric, who took a touch before curling a fine left-footed strike into the bottom corner.
Real captain Sergio Ramos grabbed his side's third goal with a powerful header from a corner before Al Ain, who shocked South American champions River Plate in the semifinals, got a late consolation goal through Japanese defender Tsukasa Shiotani.
Real could have won by more.
Colorado police arrest fiance of woman who disappeared
The arrest came after the investigation of cell phone records and data, in addition to searches of Berreth's home, officials said. Still, as authorities continue to search for a body, "it's hard to accept" that Berreth actually is dead, says Garretson.
It was a record fourth triumph in this competition for Real, with them surpassing LaLiga rivals Barcelona's tally of three wins, as boss Santiago Solari celebrated his first trophy in management.
Earlier, River beat Kashima Antlers 4-0 for third place.
Bale, scorer of a hat-trick in the semi-final victory over Kashima Antlers, nearly made it 2-0 in spectacular fashion shortly after the break, sending the ball just over with an overhead kick, and moments later a Benzema shot bounced wide. The game pits the heavily favored giant of Spanish soccer against the champion of UAE's Arabian Gulf League (and the Club World Cup's "home" team) for the right to crown itself king of the world. Gonzalo Martinez scored twice on what is expected to be his final appearance before joining MLS champions Atlanta United.