Egypt, who finish second in Group 4 with 8 points, reach the quarters for the fourth consecutive and eighth overall quarterfinal qualification.
The Pharaohs will face France in a crunch tie on Tuesday at 18:30 Cairo time (GMT+2)
The Pharaohs got off to a shaky start, struggling with uncharacteristic errors in the first half that allowed Cape Verde to seize the initiative and hold the lead for much of the opening period.
However, Egypt rallied just before halftime, edging ahead with a narrow 14-13 advantage.
Cape Verde leveled the score early in the second half, but Egypt soon regained control, steadily building momentum to pull ahead 20-18.
The team maintained their composure in the closing stages, despite a facial injury to key player Ahmed Hesham Sissa, who was substituted by coach Juan Carlos Pastor.
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