Esperance had a chance to claw back level in the 13th minute but Moataz Zaddem saw his header from close range pushed to the bar by Mohamed Elshenawy.
Ahly should have made it 2-0 in the 26th minute when Kahraba was sent through on goal brilliantly by Tau, but he placed his effort wide with only the keeper to beat.
In the second half, Esperance were off faster off the blocks, but were stunned just 10 minutes after the restart when Tau scored a brilliant curled effort from the edge of the box, after feinting his shots severally to find space.
Esperance had chances, Mohamed Ben Hamouda seeing a header fly inches wide while Mohamed Ben Romdhane had an overhead kick off a corner well saved by Elshenawy.
The hosts piled pressure on Ahly as they sought to get back into the game but while they pushed bodies forward to get an equalizer, they left spaces behind and were punished with Ahly scoring the third 15 minutes to time.
Off a text book counter attack, Aliou Dieng sent Hussein Elshahat through on the left, the latter drilling a low cross into the box with Kahraba tapping it home at the backpost.
With a three-goal advantage away from home, Ahly had the job done and the hosts couldn’t get a way back.