The Red Devils haven't won an away match in the continental competition since April 2008.
A victory by any scoreline in the return leg in Cairo would be enough for Manuel Jose's men to reach the group stage.
For a while in the first half Ahli seemed to be superior, although the first scoring chance fell to the hosts.
ZESCO could have taken the lead as early as the fourth minute with a powerful shot but goalie Ahmed Adel lived up to prominence.
Ahli's Dominique Da Silva replied with a drive from inside the area that went wide.
ZESCO had a golden chance to break the deadlock after 10 minutes with a point-blank effort but Adel bravely blocked it to keep a clean sheet.
Adel produced more praiseworthy saves after the break.
In the last 15 minutes Ahli piled up pressure upfront, looking for a late winner.
Osama Hosni was close to translating the Cairo giants' dominance into a goal but saw his header miss the target.