Costa Rica came from behind to set up an encounter with Brazil, who narrowly beat Germany earlier in the day.
Ahmed Ali gave the UAE the lead in the 33rd minute, stealing ahead of David Guzman to poke the ball past Esteban Alvarado.
But that advantage lasted just four minutes - Bryan Oviedo providing a precision cross which Josue Martinez rose to head past a flat-footed Yousif Abdulrahman.
Chances were at a premium after the break, while the UAE's attacking potency was hit when Ahmed Ali limped off and his replacement, Ali Mabkhoot, immediately wasted a gilt-edged chance.
Both sides rallied in extra-time with Ahmed Khalil and Hamdan Al Kamali testing Costa Rica goalkeeper Alvarado.
But with two minutes to go, Mohamed Fawzi was shown a straight red card for a two-footed lunge and Costa Rica took immediate advantage.
They pumped the ball into the area and after Allen Guevara's initial shot was parried, Urena netted the rebound.