The result left Zimbabwe bottom with one point from three games halfway through the group phase and effectively out of the race for a place at next year's finals in Brazil.
Egypt, who played in front of a restricted 10,000 crowd at the Borg El Arab Stadium, took a 65th minute lead through Hosni Abd Rabo's curling free kick but Knowledge Musona equalised with a half-volley from the edge of the box in the 75th.
However, a foul three minutes from time by Mohamed Salah allowed Aboutrika to tuck home the winner and keep the seven-time African champions on target for their first World Cup appearance since the 1990 finals in Italy.
Algeria beat Benin 3-1 in the day's other African qualifier.
The 10 group winners from the second round of African qualifying will go through to the final play-off stage.