Salah put Egypt ahead during the second half in Alexandria only for Arnold Bouka Moutou to equalise two minutes from the end of regular time.
Victory gave Egypt an uncatchable four-point lead over Uganda in Group E with one round of fixtures remaining.
Uganda were held 0-0 by Ghana in Kampala Saturday.
Egypt last qualified for the World Cup in 1990 with the record seven-time African champions suffering numerous heart-breaking failures since.
The desperation to qualify was so great ahead of the Congo match that Argentina-born Egypt coach Hector Cuper admitted he was taking medication for high blood pressure.
“I am taking hypertension medicine due to the stress I suffer from continuing criticism,” he told reporters without specifying who his critics were.
“Life is full of stress, but the challenge of reaching the World Cup is the toughest stress I have faced.”
Egypt also beat Congo away and Ghana and Uganda at home to accumulate 12 points, with the only loss away to Uganda.