Ibrahimi broke the deadlock with a low shot from 25-yards after 12 minutes before Akbar Imani was dismissed before the hour mark for a second bookable offence.
Al Sadd came close to a late leveller when they hit the bar in stoppage time but the Qataris will now have to overturn a one-goal deficit in Doha in two weeks' time.
The hosts were immediately on top and Hashem Beikzadeh cut into the box before firing narrowly over in the third minute.
Sepahan took the lead nine minutes later when Al Sadd only half-cleared a corner and Ibrahimi's low strike threaded a way through a crowded penalty area and into the bottom corner of the net.
Fabio Januario, whom boss Luka Bonacic had indicated prior to the encounter would not be fit to play, was named in the starting line-up and the midfielder forced Al Sadd keeper Mohamed Saqr to turn a fierce shot around the near post in the 25th minute.
Ahmad Jamshidian sprung the offside trap 11 minutes before the break but volleyed over from close range and Emad Mohammed fired wide as Sepahan were unable to turn their first-half dominance into further goals.
Sepahan's profligacy was to prove crucial as 10 minutes into the second-half, Imani was given his marching orders following a late challenge that earned the midfielder a second booking.
With a man advantage, Al Sadd were able to pin back their rivals but were unable to create any real clear-cut chances as they were let down by the quality of the final ball.
Januario, meanwhile, had a good opportunity at the other end when he found himself with just Saqr to beat but the Al Sadd stopper pulled off a good save to deny the Brazilian.
Sepahan keeper Rahman Ahmadi was off his line quickly to block Abdul Kader Keita's effort after the striker had been sent clear down the right in the 76th minute before Al Sadd almost snatched an equaliser in added time when Hasan Al Haydos' free-kick took a huge deflection off the Sepahan wall and smacked the bar with Ahmadi stranded.