They looked on course when Salah put Héctor Cúper's side ahead just after the hour, only for Arnold Bouka Moutou to equalise with his first worldwide goal.
However, the atmosphere was subdued and many fans shed tears when Congo's Arnold Bouka equalized with a half-volley after a defensive lapse with three minutes remaining.
But the Egyptians' World Cup hoodoo ended as Salah held his nerve late on.
Congo (4-2-3-1): Mouko, Badila, Etou, Itoua, Mayembo, N'Dinga, Oniangue, Bahamboula (Ndockyt 84), Bifouma, Saint-Louis (Gandze 90+2), Delarge (Moutou 71). Just after the hour mark, Salah latched on to a pass from Arsenal's Mohamed El Nenny before poking home from close range.
Murder of 4 women, guard rocks E Delhi
Joint Commissioner of Police (Eastern Range) Ravindra Yadav and Special CP (Law & Order), North Zone, SBK Singh visited the spot. Police said that a cupboard kept in the room where the women were found murdered, was ransacked, but nothing was found missing.
Thanks to Salah again who found the net deep in stoppage time via a penalty kick, to give Egypt a memorable, hard fought victory over bottom-placed Congo.
Egypt now have a four-point lead over second=placed Uganda in Group E. Their last appearance at the World Cup came in 1990, when they were drawn against England, the Republic of Ireland and the Netherlands.
The country last qualified for the 1990 World Cup in Italy.
Should he play next year, Egypt goalkeeper El Hadary could become the oldest player at a World Cup ever. The Pharaohs won the Africa Cup of Nations in 1998, 2006, 2008 and 2010, but consistently faltered in World Cup qualifying.