After a barren first half, the Black Stars upped their game in the second half and got the opener in the 62nd minute after Jordan Ayew latched on to a defence-splitting pass on the edge of the penalty box and drove in a shot to leave the goalkeeper completely stranded.
Ghana are looking to end a run of 35 years without a Cup of Nations title.
But with extra time looming, Egypt's moment came with three minutes of normal time to play.
The record seven-time champion, held back by years of political upheaval back home, returned to the last four for the first time since 2010 with an 87th-minute victor over Morocco in the last quarterfinal in Gabon.
Ghana coach Avram Grant lamented his side's first half showing but was full of praise for their second half display.
Dimitri Payet: West Ham agree transfer fee with Marseille
However the Hammers are still demanding at least £30m for Payet, while Marseille have indicated they will not pay more than £25m. Bilic's side have won five of their last seven league matches, including their last two against Crystal Palace and Middlesbrough.
Ghana will slug it out with Burkina Faso in the semi final on Wednesday to book a place in the final of AFCON 2017.
Without injured captain Asamoah Gyan they saw DR Congo hit the woodwork through Dieumerci Mbokani and then went in front in the 63rd minute when Jordan Ayew fired past Ley Matampi in the Leopards' goal.
The newly-inaugurated VEEP of Ghana, however, cautioned the team to be wary of Cameroon, as they might not be an easy team to vanquish.
It was some quality football from both the teams, which made the game interesting as Ghana once again regained the lead with Andre Ayew slotting the spot-kick, which was awarded to them after Christian Atsu was brought down with just under 13 minutes left for the game to end.
Paul-José M'Poku drew level for DR Congo, shooting from outside the 18-yard box in the 68th minute.