Egypt, who have not reached a World Cup since 1990, lead Group E with nine points from four matches, two ahead of Uganda.
Ghana have five points and remain in contention but bottom side Congo, with one point, have been eliminated. Only the top team in each group advances to the finals in Russia.
Liverpool forward Salah scrambled home a rebound in the sixth minute after his volley from Abdallah Said's chip over the Uganda defence had been saved by goalkeeper Denis Onyango.
Onyango later made a remarkable triple save from Said and Ramadan Sobhi to deny Egypt a second, while the visitors lacked penetration to trouble 44-year-old Egypt keeper Essam El Hadary.
Egypt, coached by Argentine Hector Cuper, will be confident of ending their long wait to reach a World Cup with a home match against Congo on Oct. 8 before they visit Ghana in November.
Uganda host Ghana on Oct. 7 and travel to Congo in November.
(Reporting by Nick Said; Editing by Ken Ferris)
