The Liverpool attacker chipped the ball into the net to complete the scoring in a seesaw match day five struggle during which both sides led.
Salah has scored four goals in qualifiers for the Cup of Nations, which is two less than leader Idion Ighalo of Nigeria.
Naim Sliti gave Tunisia an early lead that Mahmoud Hassan cancelled out before the interval at the 86,000-capacity Borg el Arab stadium in Alexandria.
Baher el Mohamady nodded Egypt in front on the hour only for Sliti to score again with eighteen minutes remaining and a draw seemed likely until Salah struck.
Before flying to Egypt, Salah continued a return to form after a slow start to the English Premier League season by scoring the first goal for Liverpool in a 2-0 win over Fulham.
It was his sixth league goal of the season, two fewer than leading scorer Sergio Aguero of Manchester City.
Salah had a sensational maiden campaign with Liverpool, scoring 44 goals in all competitions in 2017/2018 after moving from Roma.
Victory brought Egypt level with Tunisia in Group J on 12 points but the losers retained first place on head-to-head records.
Tunisia entered the match as the only team among the 48 in the qualifying competition boasting a 100-percent record, having beaten Egypt at home, eSwatini away and Niger twice.
It was the first match in charge for Tunisian co-caretaker coaches Mourad Okbi and Maher Kanzari after veteran Faouzi Benzarti was sacked despite delivering four victories.
Madagascar, Senegal and hosts Cameroon have also qualified for the 2019 Cup of Nations - the first to feature 24 teams - and another fifteen countries could secure places this weekend.
Meanwhile, Burundi climbed above Mali and Gabon to top Group C with a 5-2 win over South Sudan in Juba, where Fiston Abdul Razak scored four goals for the visitors.
A close first half ended with the Burundians leading 2-1 as Razak scored, Atak Lual equalised and Cedric Amissi put the east Africans ahead for a second time.
Dominic Aboy brought pointless South Sudan level again before Razak netted three times in eleven minutes for Burundi, who have seeking a first Cup of Nations appearance.
Burundi have nine points, Mali eight, Gabon seven and South Sudan none with the second and third-place teams meeting in Libreville Saturday.
The top two finishers qualify and a Malian victory over Gabon would assure them of a place at the tournament that takes place in Cameroon between 15 June and 13 July.