Ashour, who also scored and dished out an assist in Zamalek's exciting 3-2 win over Pyramids FC last Wednesday, netted with a trademark long-range shot two minutes before the break as the White Knights secured their fourth straight win and their second under new coach Jesualdo Ferreira.
Zamalek had key winger Achraf Bencharki sent off early in the second half following a VAR review, with the Moroccan paying the price of a reckless high-foot challenge.
But they survived some late attempts from the struggling Maqassa to secure a precious victory, especially after leaders and perennial Cairo rivals Ahly suffered a stunning 1-0 loss to Masry.
Zamalek moved level on 31 points with Ahly, although the latter still have a game in hand. Maqassa remain second from bottom with nine points, two adrift of the safety zone.
Early penalty
Zamalek could have taken a seventh-minute lead after being awarded a penalty for a handball but spot-kick specialist Ahmed Zizo had his effort saved by keeper Mohamed Magdi, who dived the right way.
It was Zizo's second straight wasted penalty after he also failed to hit the target during Egypt's bitter shootout loss to Senegal in the second leg of a World Cup qualifying playoff last month.
At the other end, Maqassa's Karim Halawa went close with a curling shot but Zamalek quickly re-assumed control, with lone striker Omar El-Said heading over from a good scoring opposition.
The breakthrough came on 43 minutes when Ashour's skidding shot from 25 meters beat Magdi.
Zamalek were expected to open the floodgates after taking the lead but Bencharki's dismissal forced them to change their tactics and tighten up at the back, with Ferreira playing with a five-man backline to stifle Maqassa's attacking attempts.
Maqassa's best chance saw forward Mahmoud Fahmi head just wide from a floated cross after keeper Mohamed Abou-Gabal had mis-timed his jump.
They also whipped in some dangerous crosses towards the end but Zamalek held on to continue their recent fine run in the premier domestic competition.
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