Kwesi Appiah's men had emerged as 6-1 victors from the first encounter, but went behind to Amr Zaki's opener midway through the first half as Egypt played in front of their home fans for the first time in almost two years following the Port Said riots and ousting of President Mohammed Morsi.
However, Zaki's strike failed to inspire an Egyptian fightback as the hosts had to wait until the 83rd minute for a second through Gedo before Kevin-Prince Boateng pulled a goal back for Ghana late on.
The comprehensive 7-3 aggregate win means Ghana have qualified for their third consecutive World Cup, while Egypt have not made the finals since 1990.
Bob Bradley made five changes to the Egypt side that crumbled to a 6-1 defeat in the first leg, with Zaki, Kahraba and Ramy Rabia among those to come in, while Harrison Afful replaced Samuel Inkoom in the only Ghanaian alteration from the opening encounter.
Zaki let fly from the edge of the penalty area in the opening minutes, but fired his effort straight at Ghana goalkeeper Fatau Dauda.
Rashid Sumaila then went close to dashing the visitors' slim qualification hopes after six minutes when he drilled a low effort narrowly wide of the target from 18 yards.
But it was Egypt who took the lead in the 25th minute when Zaki bundled over the line from close range after Dauda failed to deal with a Mohamed Aboutrika free-kick from the right.
Ghana's players were subjected to a barrage of distracting laser pens as the home fans tried to play their part in influencing an unlikely comeback, and Egypt continued to have the better of the chances - an inspired Zaki forcing Dauda to tip over from distance 10 minutes prior to the break.
The hosts maintained a high tempo for the remainder of the opening period, but were unable to breach the Ghanaian defence, leaving them in need of five second-half goals.
Mohamed Salah tried to curl in an effort from the edge of the penalty area shortly after the interval, but sent the ball high and wide of the target.
As time ticked away, Egypt looked decreasingly likely to reduce the deficit as Ghana became content to defend their aggregate advantage.
Sulley Muntari went close to levelling the encounter on the night in the 63rd minute, but his low strike whistled beyond the post and was one of few chances in second period.
With the result already beyond doubt, Jerry Akaminko was forced to clear off the line for the visitors after a penalty-area scramble in the 75th minute.
Gedo drilled home a second for the hosts from close range in the 83rd minute only for Ghana's qualification party to start among their fans one minute from time as Boateng tapped home from an Asamoah Gyan cross.
