Gedo fired in Al Ahly's opener from 12 yards shortly before half-time and Walid Soliman doubled their lead just after the hour mark.
Esperance's Yannick N'djeng pulled a goal back to set up a tense finish.
Al Ahly had Mohamed Aboutrika's late penalty saved but held on to become African champions for a seventh time.
Hossam Ghaly lifted the trophy to seal a remarkable win amide a domestic season in Egypt that has been postponed indefinitely because of the February stadium riots that left 74 people dead.
Al Ahly, who extended their own record for the most African Champions League wins, will represent the continent at the Fifa Club World Cup in Japan next month.
Esperance fielded a weakened side because of suspensions and injuries, although Youssef Msakni returned to the team despite having had an operation for appendicitis two weeks ago.
The Tunisian side were the more defensive in a first half that produced some flowing football but few goalscoring opportunities.
Ahly were rewarded for their purpose when Gedo struck on 43 minutes after good work down the left from Hamdy Al-Sayed, who shook off a defender and cut the ball back from the goal-line.
Esperance came into the second half with more urgency, and N'djeng had a shot saved on 53 minutes.
Soliman made it 2-0 in the 61st minute, hooking the ball over the head of Esperance defender Mohamed Ben Mansour to leave himself one-on-one with the keeper on the edge of the box before shooting into the bottom-right corner.
N'djeng then hit the post, before finally getting his goal with six minutes to go, side-footing in from six yards - but Esperance still needed two more goals if they were to retain their title.
Ahly legend Aboutrika had his penalty pushed past the post by Esperance keeper Moez Ben Cherifia, who had fouled Ahly's Mauritania striker Dominique Da Silva.