Sameh Mahmoud broke the deadlock in the 52nd minute when he poked past keeper Mahdi Soliman, who unwisely advanced in an attempt to keep a clean sheet.
Ernest Papa Arko doubled the military side's lead in stoppage time upon converting a penalty kick.
Gaish are now in second place with 24 points, while ENPPI are seventh on 16.
After losing their two opening games, Farouk Gaafar's side notably improved and enjoyed a string of satisfying results.
Visitors ENPPI played without the guidance of their coach Diaa Al-Sayed, who was hospitalized several minutes before the game after suffering sudden deterioration in his health condition.
FilGoal.com understands that Al-Sayed was released from hospital several hours later.
Al-Sayed suffered from extremely high pressure, exhaustion and flu.
The match's goals