The Iranian side looked to dominate from the start but Al Jazira succeeded in keeping it at bay for most of the first half, but Persepolis forward Ali Alipour broke the host’s resilience in the 42nd minute, heading in Vahid Amiri’s cross into the top right corner to put the visiting team in front.
In the 52nd minute, Ali Mabkhout dribbled through the Persepolis defense and struck a powerful effort that hit the back of the net.
The host added a second through Romarinho, who received Mabkhout's pass and quickly advanced into the area before slotting home in the 77th minute.
Persepolis responded instantly from the spot as Godwin Mensha converted on his second attempt after reacting quickest to Ali Khaseif's save from his penalty kick six minutes from time.
Just as the Iranians thought they had come back from Abu Dhabi with a 2-2 draw, defender Khalifa Mubarak won it for Al Jazira with a last-gasp goal, directing his header from Mbark Boussoufa's free-kick into the back of the net in the final minute of added time to give the Emirati side a slight advantage going into the second leg.
Persepolis, however, will be encouraged by its two away goals going into next week's return leg in Azadi Stadium in Tehran.