The win means Egypt now hold an unassailable lead on 12 points, become the second African team after Nigeria to qualify for next year’s World Cup with a game to spare.
After a 0-0 first half, Salah eventually calmed the Egyptian fans nerves by breaking the deadlock in the 63rd minute.
With just three minutes left, Congo equalised through Moutou.
But in the 95th minute, Egypt were awarded a penalty which Salah converted to send the whole nation into wild jubilation.
Their last group fixture is an inconsequential game away to Ghana while Congo will entertain Uganda.