Zinedine Zidane's charges thought they had taken the lead on 30 minutes through Casemiro but the referee's initial decision was overruled by the Video Assistant Referee (VAR). Real Madrid tried to score the first goal to have the upper hand in the game but Al Jazira's goalkeeper, Ali Khasif, saved all their chances.
Madrid will try to win its third world title in four seasons when its faces South American champion Gremio of Brazil on Saturday.
The Wales worldwide came off the bench to score with his first touch in the 81st minute in Abu Dhabi, after Cristiano Ronaldo had cancelled out Romarinho's shock opener.
Despite Real dominating the match at the Zayed Sports City Stadium in Abu Dhabi, it was the hosts who took a shock 41st-minute lead through Romarinho.
Zidane said on realmadrid.com: 'We deserved the win and a place in the final.
The Welshman came off the bench with ten minutes remaining and took just seconds to fire in what would prove to be the eventual victor. "It takes some time but I will be working as hard as I can on and off the pitch to get where I want to be".
Cue Gareth Bale. Coming on the 80th minute, just seconds later he put Real Madrid 2-1 ahead with a low finish inside the box.
"The issue of video review is not something that is up to me to decide, but I think football is better off without it", Bale said.