Goals from Marcos Llorente (60th minute) and Sergio Ramos (79th) gave the LaLiga giants 3-0 lead as the game reached the homestretch before Al-Ain's Tsukasa Shiotani netted their consolatory goal in the 86th minute.
The win sealed a third consecutive World Club Cup title for Real Madrid, and this fourth triumph takes them one better than their rivals, Barcelona, in the FIFA-organised competition that started in 2000.
"A dream year, really".
Modric, victor of the Ballon d'Or, World Cup Golden Ball and FIFA's The Best Men's Player prize, scored his first Madrid goal since January to start the rout.
Solari admitted that "Al Ain's performance was great".
Real Madrid then had numerous additional opportunities to score over the remainder of the first half, but a shot by Lucas Vasquez grazed the woodwork and Karim Benzema sent a close-range shot over the crossbar.
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In its current format, Real Madrid have won each of the four Club World Cup finals they have played in.
But the rest of the match, Madrid lived up to their elite status and the talent gap was evident between the sides. It was his first goal for Madrid, as he continues to impress playing for the injured Casemiro in recent weeks. Real have won 11 of those games, lost twice and qualified for the last 16 of the Champions League.
The tsunami struck the Sunda Strait, which sits between the islands of Java and Sumatra, on Saturday night.
Khalid Issa, Al Ain goalkeeper, said that Al Ain is looking forward to the coming seasons, as its players still aim for more success.
The cause of the tsunami has not been determined but the Indonesian National Board for Disaster Management said an undersea landslide linked to the eruption of nearby Anak Krakatoa was a possibility, reports Efe news. In 2014, Real Madrid defeated San Lorenzo 2-0, which became his first of the four FIFA World Cup title wins with Los Blancos.