Going into the game with no option but to beat the Cranes, it took Egypt just six minutes to score via Salah, whose sixth-minute goal eventually proved the winner.
Having surrendered top spot after their defeat to the very opponent in Kampala just a few days ago, Egypt have now returned to the summit top with nine points - two ahead of second-placed Uganda.
Egypt will now be hoping once-group rivals Ghana, who thrashed Congo 5-1 earlier in the day, defeat or even hold Uganda to a draw on October 7 in Kampala, just a day before the Pharaohs meet Congo at home.
Should the Ugandans fail to prevail against Ghana and Egypt overcome basement side Congo, Hector Cuper's men will be sure of a World Cup berth next year in Russia regardless of the result of their final group game with Ghana.
Egypt have yet to make a single World Cup appearance since last reaching the prestigious competition in 1990.
Early Salah winner
Following a short spell of dominance by Uganda early in the game, it was the hosts who eventually took the lead when a superb through ball from Abdallah El-Said coupled with an excellent run from Salah ended up with the latter giving his side the lead.
Despite facing a weak opposition, Egypt boss Cuper was reluctant to change his usual strategy and chase the ball in advanced positions in search of the second, leaving the Ugandan backline free on the ball.
But it was the home side who posed real threat on goal and came close to doubling their lead if it was not for in-form keeper Denis Onyango, who pulled off a couple of superb saves in quick succession to deny El-Said and Stoke City winger Ramadan Sobhi.
Uganda was unable to penetrate the Egypt block, lacking the needed accuracy in their passing combinations in the final third to round off their counter attacks successfully.
Egypt squander the second
The second half did not bring an entirely different affair, with both sides alternating spells of possession after the restart.
Uganda looked somewhat likely to pose danger from set-pieces, while Egypt had sporadically threatened, particularly through substitute Mahmoud Hassan Trezeguet and goal-scorer Salah.
With the pacey Salah capitalizing on space down the right, his forthcoming cross eventually found Trezeguet who failed to find the net from inside the area when it looked to easy to score in the 75th minute.
Playmaker El-Said continued squandering easy chances, with a promising counter-attack ending up with the Ahly man blasting high over the bar in the 85th minute.
And Salah came close to scoring just two minutes from regular time when he cut inside onto his stronger left foot, but saw his effort go narrowly wide of the post as Egypt came up 1-0 victorious to move a step closer towards realizing their World Cup dream.
Source: Ghana soccer net