Cristiano Ronaldo levelled for hte European champions 10 minutes after the pause and Gareth Bale came off the bench to score the winner.
"It's great to get the goal," Bale told Real Madrid TV. "When you come on you want to make an impact, but the most important thing is to win and be in the final."
Real will go for their fifth trophy of the year when they face Brazilian side Gremio on Saturday.
Bale was making only his second substitute appearance since September due to a series of muscle injuries.
"I need to be patient, said the I've had some problems and it takes time. I need to listen to my body," said the 28-year-old Wales international. Al Jazira, invited to the competition as champions of the host country, went in at half time with the lead.
A poor clearance from Nacho gifted possession and Romarinho showed great composure to cut inside and curl his shot inside Keylor Navas's far post.
Zinedine Zidane's men drew level eight minutes later when Luka Modric set up Cristiano Ronaldo to smash a shot past Al Jazira goalkeeper Khaled Al Senaani;
Madrid turned up the pressure but the misfiring Karim Benzema shot straight at Al Senaani then hit the post with two other good chances. He was eventually replaced by Bale. He atoned for the earlier profligacy as he slotted home Lucas Vazquez's cutback.
Madrid won the competition in 2014 and 2016 and a third success on Saturday would take them equal with Barcelona for the record amount of tournament wins