An own goal by defender Dario Khan, his second at the finals, and a left-foot volley from substitute Mohamed Nagui put Egypt in the quarter-finals.
The defending champions also created a Nations Cup finals record of 15 unbeaten matches stretching back to 2004, beating the previous mark set by Cameroon between 1984-88.
Khan knocked the ball past his own goalkeeper, as he did against Benin last Tuesday, in a mix-up after fellow defender Mexer missed a cross by Ahmed Fathi.
The 46th minute own-goal came after Mozambique had soaked up relentless first-half pressure.
Nagui made it 2-0 with a stunning volley from just inside the penalty area in the 80th minute, initially failing to control a pass with his right foot but swivelling to thump the loose ball into the net.
"The result allows us to maybe give some other players a chance in the next match," Egypt assistant coach Shawki Gharib told reporters.
The holders next meet Benin in Benguela on Wednesday. With one game left to go in the group, Egypt's six-point haul can only be matched by Nigeria.
If the two teams finish on the same points Egypt will be top because of their 3-1 win over Nigeria last Tuesday.
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