Their hopes of ensuring top place in Group G and advancing to the last phase of the African preliminaries were put on hold, however, when Guinea beat Mozambique 6-1 in the group's other game.
The goals from the 20-year-old Salah, who plays at Swiss champions FC Basel, confirmed his emergence as a new hero for Egyptian football.
Mohamed Aboutrika, who has for a decade been a talismanic performer for the Pharaohs, opened the scoring after only six minutes and proved the perfect foil for Salah to add another three.
Egypt, the only African side with a 100 per cent record, advanced onto 12 points with two games to play, five ahead of Guinea.
Islam Slimani scored twice as Algeria came from behind to score a significant 3-1 away win over Benin in Porto Novo, taking over top place in Group H after Mali were held to a surprise home draw by lowly Rwanda in Bamako.
Rudy Gestede, who won recent promotion to the top flight in England with Cardiff City, scored in only his second international to put Benin ahead.
Slimani then scored twice in the space of four minutes before the break to turn around the tie.
Togo again had to do without Emmanuel Adebayor but got their first win of the campaign by beating Cameroon 2-0 in Lome. The win put Togo suddenly in contention in Group I, albeit two points behind the co-leaders Libya and Cameroon.
There was also a first win in Group E for Burkina Faso, runners-up at the African Nations Cup finals at the start of the year.
Jonathan Pitroipa, voted best player of the tournament in South Africa, scored nine minutes from time away against Niger in Niamey. But the Burkinabe are still four points behind leaders Congo with two rounds to play.
The next round of fixtures are scheduled for Wednesday and the coming weekend with the last group matches played in September.
The 10 group winners go through to play-offs in October and November to determine the five African qualifiers for Brazil.