Amr el Soulia scored the other goal for the hosts before a 60,000 crowd at the Borg el Arab Stadium in Alexandria and Youcef Belaili converted a penalty for Esperance.
Ahly have won their last three away matches against Esperance in the premier African club competition and are favoured to lift the trophy a record-extending ninth time after the return leg next Friday.
VAR (video assistant referees) was being used for the first time in a Champions League final and Algerian referee Mehdi Charef twice used the system to rubber-stamp his decisions.
Esperance goalkeeper Moez Ben Cherifia made contact with Ahly striker Walid Azaro and the match official pointed to the spot before watching replays and confirming the spot-kick.
Cherifia correctly guessed the direction of the shot, but veteran Soliman struck it too hard and too high for the goalkeeper to have any chance.
The goal on 34 minutes gave the Cairo Red Devils a 1-0 half-time advantage that they doubled after 58 minutes through El Soulia.
Soliman was the creator, crossing the ball low into the heart of the goalmouth where El Soulia controlled it with his first touch, then poked it past Cherifia.
Rattled two-time champions Esperance clawed their way back into the game after 64 minutes via the only penalty of the three in which the match official did not use VAR.
Goalkeeper Mohamed el Shenawy clearly fouled Youcef Belaili with his shoulder and the Algerian struck the spot-kick under the body of the Ahly shot-stopper to halve the deficit.
But when an Esperance defender retaliated against Azaro in the box, the referee once again pointed to the spot and ran to the touchline monitor before confirming his decision.
Cherifia believed Soliman would aim for the same corner, but the veteran outfoxed him with a calmly-struck penalty to the other side on 77 minutes.
Both sides were foiled by the woodwork -- Ghilane Chaalali for Esperance just before half-time and Soliman from a free-kick soon after his second goal.
The VAR penalties added to the drama in a match that was not for the purist with 48 fouls, five yellow cards and several head injuries preventing any rhythm developing.
Esperance captain Khalil Chemmam had to leave the field temporarily just before half-time with his face covered in blood from a head wound and Soliman also needed lengthy treatment.
Ahly winger Ayman Hamoudy was the victim of a late challenge in the second half and, although obviously dazed, continued for a while before being substituted.
It was a match that bordered on the brutal at times with both clubs desperate to become champions, pocket $2.5 million (2.2 mn euros) and secure a FIFA Club World Cup place.
Esperance began and finished strongly with El Shenawy having to be at his sharpest in the dying minutes to avoid conceding a second goal.