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Salah's 69th minute effort came despite a largely anonymous performance from the Egyptian forward as his team battled to beat the minnows from west Africa.
The result was clouded in controversy as Guinea Bissau had a late equaliser ruled out after a VAR check. Mama Balde thought he had scored with a screamer from a tight angle to level in the 82nd but the referee, after consulting the pitchside monitor, decided he had fouled a defender in the build-up to the goal.
It looked a harsh decision, leaving Guinea Bissau still without a goal in their last six finals matches stretching back to 2017 and now with slim hopes of progressing. They have one point.
"It was a tough game, we just did it at the end. We were a bit lucky with the foul," said Salah.
Egypt needed the win after losing their opening Group D game against Nigeria, provoking loud criticism from pundits and supporters back home.
Salah struck the outside of the post in the second minute suggesting it might be a one-sided affair against a team 61 places below them in the FIFA rankings, but the closest Egypt came after that in the first half was when Mostafa Mohamed also hit his shot against the upright.
After Salah's goal, Ahmed Zizo struck the post again but Guinea Bissau showed little regarded for the seven-time African champions with Balde scoring from a tight angle.
But he was adjudged to have pulled back fullback Omar Kamal as he battled to get into a scoring position.
"We just needed to win the game to concentrate on going as far as we can in the tournament. As you can see, it's a very hard tournament, it's going to be tough but we'll do our best," added Salah.
Egypt finish the opening round against Sudan in Yaounde next Wednesday while Guinea Bissau take on group leaders Nigeria in Garoua at the same time.