The Liverpool forward continued what has been a prolific season at club level so far by taking his international tally up to 55 goals in 94 games - only five African players have ever scored more.
Fifteen of those goals have now come in World Cup qualifying matches too, seeing him surpass Mohamed Aboutrika as Egypt's highest-ever scorer in such games.
Salah scored each of the first four goals for his side in Cairo, including two in the space of five minutes midway through the first half - the second of those coming from the penalty spot.
The 31-year-old completed his hat-trick just three minutes into the second half, before adding a fourth in the 69th minute.
Egypt then completed the rout through goals from Mostafa Mohamed and Trezeguet as their bid to reach the 2026 World Cup got off to a perfect start.
The same was not true for another of Africa's giants, with Nigeria being held to a 1-1 draw by Lesotho, ranked 113 places below them in the FIFA rankings.
Elsewhere, Islam Slimani was among the scorers as Algeria beat Somalia, while there were also victories for Gabon, Mozambique and Burundi.