Zamalek struggled to break down the visitors' massed ranks in the first half at Cairo's International Stadium but got the job done after the break to set up another two-legged tie against Burundi's Flambeau du Centre for a place in the group stage.
Veteran schemer Mahmoud Shikabala, who scored a superb opener in Zamalek's 2-0 first-leg win, had the team's only chance in the first period when he volleyed just over the bar from inside the area.
Elect-Sport could have stunned their illustrious opponents on 37 minutes when Djoeta Frederic was picked out unmarked in the area but he blasted his shot high over with the goal at his mercy.
The second half was also a low-tempo affair but Zamalek finally broke the deadlock when they were awarded a penalty for a challenge on marauding left-back Abdallah Gomaa in the 71st minute.
Spot-kick specialist Ahmed Zizo, who also found the net in the first leg, sent the keeper the wrong way to kill off the game as a contest.
Central defender Mahmoud El-Wensh added the second eight minutes later when he nodded in from close range at the far post after playmaker Youssef Ibrahim flicked a corner into his path.
Zamalek are seeking to win the Champions League title for the first time since winning the last of their five crowns in 2002.
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