Aston Villa defender Elmohamady and Liverpool's African Player of the Year Salah both struck first-half goals in Cairo for the Pharaohs who followed Nigeria into the knockout stage.
Egypt, winners in 2006, 2008 and 2010 and beaten by Cameroon in the 2017 final, beat Zimbabwe in their opening match and are top of Group A.
But they did not have it all their own way against DR Congo, who twice hit the woodwork.
Marcel Tisserand crashed his effort against the woodwork from six yards in the 11th minute after Tresor Mputu's corner had been flicked on.
Egypt opened the scoring in the 25th minute when Elmohamady stabbed the ball home from inside the penalty area after DR Congo had failed to clear Salah's cross.
Salah's 25-yard free-kick was then turned away by goalkeeper Ley Matampi before Tisserand just failed to get on the end of Mputu's excellent cross at the other end.
DR Congo hit the crossbar again in the 40th minute through Jonathan Bolingi's header, but Salah made it 2-0 to the hosts three minutes later with a searing shot inside the near post.
The Leopards pressed for a way back into the match in the second period, enjoying decent spells of possession only for their end product to let them down.
Yannick Bolasie went closest to breaching the Egypt defence when his fiercely-struck free-kick curled narrowly wide in the closing stages.