Recently crowned Ballon d'Or winner Modric took one touch before thumping the ball into the bottom corner from outside the box to break the deadlock in the 14th minute after Al Ain had missed two early chances to take a shock lead.
Madrid's home-grown midfielder Marcos Llorente doubled the European champions' lead on the hour-mark with a superbly struck volley from outside the area.
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 semi-finals, got a late consolation goal through Japanese defender Tsukasa Shiotani.
Madrid substitute Vinicius Jr. burst through in stoppage time and fired in a shot which defender Yahia Nader diverted into his own net.
Real have won the last three editions of the tournament, also lifting the trophy in 2014, and moved ahead of Barcelona as the team to have won it the most times.
"We're very happy, these players deserve this," said Real coach Santiago Solari after winning his first piece of silverware since replacing Julen Lopetegui in the dugout in October.
"This is the icing on the cake of winning the Champions League three years in a row. It's a great feat for the club, this group and the other coaches, and we can't forget we're here thanks to the work of Zinedine Zidane. It's going to be difficult for any team to do what this side has done."
Al Ain coach Zoran Mamic said Real were far too good for his side despite creating those early chances which forward Hussein El Shahat squandered, missing the target with one effort and seeing Ramos clear his shot off the line moments later.
"We have to congratulate Real Madrid because they won this game deservedly, by playing good football, and we couldn't compete with them," said the Croatian.
"It's the fourth game we've played in only a few days and it has taken its toll on us, but we have had a great tournament. No-one expected us to get to this point."
(Reporting by Richard Martin; editing by Martyn Herman and Clare Fallon)
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