Nigeria knew only a win would guarantee their place in the last eight after opening the tournament with a surprise defeat to Malawi before edging Zambia in their second match.
The defending champions responded with their best performance of the competition, producing an impressive attacking display to overwhelm Egypt.
Asisat Oshoala settled any early nerves when she converted a penalty in the 21st minute to put Nigeria ahead.
Gift Monday doubled the lead in first-half stoppage time after good work from Rinsola Babajide, but Egypt stayed in the contest when Nadine Ghazi scored from the penalty spot deep into added time to leave the score at 2-1 at the break.
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Nigeria quickly regained control after half-time. Babajide claimed her second assist of the night as Uchenna Kanu restored the two-goal advantage in the 57th minute.
Christy Ucheibe made it 4-1 from another penalty before Ghazi grabbed her second goal for Egypt in the 84th minute.
There was still time for Nigeria to add two more goals in stoppage time. Rasheedat Ajibade converted a penalty before providing the assist for Joy Omewa to complete an emphatic 6-2 victory.
The result ensured the Super Falcons reached the quarter-finals after recovering from a difficult start to their title defence.