They were joined in the last four by Egypt, who later rode their luck to defeat Morocco 1-0 in Port Gentil with a late strike from substitute Mahmoud Kahraba, the first time in 31 years they have beaten their north African rivals.
Seven-time winners Egypt, back at the continental finals for the first time since lifting the trophy in 2010, will face Burkina Faso in their semi-final on Wednesday in Libreville.
Ghana will have an extra day to rest and plot victory over Cameroon in Franceville on Thursday having reached the last four for the sixth time in a row.
All the goals in their quarter-final with the Congolese came in a 15-minute spell in the second half.
Ghana were ahead when Mubarak Wakaso picked out Jordan Ayew and he sprinted to the edge of the box before unleashing a fierce shot past Congolese goalkeeper Ley Matampi.
It was a goal of high quality, but the equaliser from Paul-Jose Mpoku was even better as the Panathinaikos winger took aim from 30 metres and found the top corner of the net.
Congo were the architects of their own downfall after that though as defender Joyce Lomalisa clumsily fouled Christian Atsu in the box and Andre Ayew converted the penalty.
Ghana coach Avram Grant lamented his side’s first half showing but was full of praise for their second half display.
“We corrected mistakes we made and in the second period it was totally different,” Grant told reporters. “We played good football. The two goals we scored were fantastic. And when we fell asleep, they (DR Congo) also scored a fantastic goal.”
Morocco should have buried Egypt long before the closing stages of their game and were made to pay for that profligacy when Kahraba bundled the ball home from a corner.
Morocco’s Mbark Boussoufa had earlier curled a shot from outside the box against the crossbar and striker Aziz Bouhaddouz missed a sitter from close range.
Egypt coach Hector Cuper is likely to be without Mohamed Elneny and fellow midfielder Mohamed Mohsen for their semi.
“Mohsen looks to have a serious problem with a knee,” Cuper said. “Elneny has a bad calf strain. He will have tests and we hope if we manage to reach the final that he can return.”
(Reporting by Nick Said; Editing by Ken Ferris)