A single Ali Mabkhout goal in the second half from a pass supplied by Romarinho was the difference between the teams.
Madrid fly to UAE on Sunday having trashed Sevilla 5-0 in their final La Liga game before commencing their FIFA Club World Cup campaign.
Former Madrid star Lassana Diarra is on the books of Al Jazira but is not included in their squad for this tournament. He is expected to depart the club in the next transfer window.
In the other semi-final, Copa Libertadores champions Gremio will play Mexico's Pachuca on Tuesday in Al Ain. Pachuca qualified for the semis after winning the CONCACAF Champions League and beating African representatives Wydad Casablanca in the quarter-finals.