The Liverpool star chipped the ball into the net to complete the scoring in a seesaw matchday 5 struggle during which both sides led.
Salah has scored four goals in Cup of Nations qualifiers -- two less than chart-topper Odion Ighalo of Nigeria.
Naim Sliti gave Tunisia an early lead that Mahmoud 'Trezeguet' Hassan cancelled before half-time at the 86,000-seat Borg el Arab stadium in Alexandria.
Baher el Mohamad nodded Egypt in front on the hour only for Sliti to score again with 18 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 this season, and eighth for his club in all competitions.
Salah had a sensational first season with Liverpool, scoring 44 goals in all competitions in the 2017/2018 campaign after joining 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 axed 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 15 countries could secure places this weekend.
Morocco are almost certain to be among the finalists after a second-half brace from Ajax Amsterdam midfielder Hakim Ziyech brought a 2-0 win over Cameroon in Casablanca.
With Cameroon qualifying automatically from Group B as hosts, Morocco have a six-point advantage over Malawi for the other qualifying place.
Malawi will have to win away to out-of-contention Comoros Saturday and then achieve an unlikely four-goal home victory over the Moroccans next March to finish second.
Ziyech converted a 54th-minute penalty to put the Atlas Lions ahead and netted again on 66 minutes.
Cameroon, suffering their first loss in four matches since Dutch coach Clarence Seedorf took charge, were reduced to 10 men on 80 minutes when Karl Toko Ekambi was sent off.
In Juba, Burundi climbed above Mali and Gabon to top Group C with a 5-2 win over South Sudan as Fiston Abdul Razak scored four goals.
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 a second time.
Dominic Aboy brought bottom team South Sudan level again before Razak netted three times in 11 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 June 15-July 13 tournament.