Al Ain converted all five of their spot-kicks in the shootout before Argentina midfielder Enzo Perez saw his effort saved by Eisa to send the hosts through to Saturday’s final in Abu Dhabi.
“I hope not to be the Croatia of this World Cup because I hope to do better. They lost the final and I want to win it,” said Al Ain’s Croatian coach Zoran Mamic.
“Maybe it’s something an Emirati must say. I’ve been in this country for a couple of years, but I think yes, that we are perhaps looking at the greatest success in football in this country. I’m proud to be part of this success. I hope the best is yet to come.”
European champions Real, who are chasing a third successive Club World Cup crown, meet Asian champions Kashima Antlers of Japan in the second semi-final on Wednesday.
Earlier, African champions Esperance defeated Mexico’s CD Guadalajara 6-5 on penalties to claim fifth place following a 1-1 draw in Al Ain.
Walter Sandoval converted an early penalty to give CONCACAF champions Guadalajara the lead, but Tunisian side Esperance leveled before half-time through a Mohammed Belaili spot-kick.