Mahmoud Fathallah opened the scoring with a far-post header after 56 minutes and Mohamed Zidan set up the second goal nine minutes later in the Group G encounter.
Zidan, who came on as a second-half substitute to pep up an ineffective home attack in an eerie atmosphere at the empty Borj Al Arab Stadium, thumped a shot against the crossbar and the ball bounced into the net off the back of goalkeeper Kampagno.
The Egyptian government ordered the match to be played behind closed doors due to security concerns.
There has been no football in the country, apart from games in the pan-African club competition, since February's attack at the Port Said Stadium where 74 fans were killed.
Friday's match marked the competitive debut for Egypt's American coach Bob Bradley.
Both countries play another qualifier next week when Egypt travel to Guinea and Mozambique host Zimbabwe.