Salah's first-time finish at the back post in the 69th minute in Garoua got his and Egypt's campaign in Cameroon up and running after they had lost 1-0 to Nigeria in their opening Group D game.
However, Guinea-Bissau were left fuming after a stunning 82nd-minute strike by Mama Balde was ruled out following a VAR review.
Carlos Queiroz's Egypt, who also hit the woodwork three times, now need only draw their last group game against neighbours Sudan in Yaounde on Wednesday to guarantee safe passage to the last 16.
"It was a really tough game and we were a little bit lucky with the foul," Salah admitted to broadcasters.
"We have to win our next game now to make sure we qualify and we will do our best to go as far as we can in the tournament."
Salah, who had not scored in any of his previous six appearances for Egypt this season, struck the post with just 84 seconds played and Mostafa Mohamed hit the same upright later in the first half.
The Liverpool star finally broke the deadlock midway through the second half when he met Amr El Solia's floated ball to the back post with a first-time cushioned volley that beat Guinea-Bissau goalkeeper Jonas Mendes.
Substitute Zizo also hit the woodwork for Egypt before Balde's superb strike into the far corner was ruled out by the referee on review for grappling defender Omar Kamal to the ground.
The small west African nation of Guinea-Bissau are appearing at their third straight AFCON having never qualified before 2017, but they are left still searching for their first win at the tournament after eight attempts.
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