Mané was mobbed by teammates after sweeping in the third goal in the fifth minute of injury time on Friday, capping an impressive performance after Ismaïla Sarr scored one goal and set up another for the Lions of Teranga.
Senegal moved to the top of Group C with successive wins and are assured of finishing among the top two.
"We've played two games. We have seven. It's important to stay focused," Senegal coach Aliou Cissé said.
Five-time champions Cameroon's progress hinge on beating bottom-of-the-table Gambia and a favour from Senegal against second-placed Guinea in their final group games on Tuesday.
Guinea are virtually assured of progress after Aguibou Camara secured a 1-0 win over Gambia in Friday's late game.
Manchester United goalkeeper André Onana started for Cameroon after missing the team's first game against Guinea because of his late arrival. His first significant contribution was to send an attempted pass out of play.
The game started with, it seemed, most fans still trying to make their way into Charles Konan Banny Stadium.
Senegal's strong start was rewarded in the 16th minute when Sarr turned to fire inside the right post after Onana failed to clear a corner.
Long lines of fans were still waiting to enter the stadium when the game paused after 30 minutes for a cooling break.
When the game resumed, Senegal remained dominant. Kalidou Koulibaly and his defence snuffed out any opportunities for Cameroon.
Cameroon defender Enzo Tchato needed to step in to block a good chance for Mané before the break, and Tolo Nouhou produced a fine tackle after that to stop Abdou Diallo.
Senegal did not enjoy the same superiority in the second half, so when Habib Diallo slide in to meet Sarr's low cross in the 71st it provided relief for the many Senegalese fans who had by now made their way into the stadium.
Jean-Charles Castelletto scored Cameroon's consolation in the 83rd before Mané made sure of the win.
Cape Verde became the first country to reach the knockout stage with a comfortable 3-0 win over Mozambique earlier.
Goals from Bebé, Ryan Mendes and Kevin Pina gave the Blue Sharks their second win from two games to finish on top of Group B above heavyweights Egypt and Ghana with a game to spare.
Cape Verde have six points, followed by Egypt on two, with Ghana and Mozambique both on one point before the final group games on Monday. The top two in each group are assured of progress, while the four best third-place finishers in the six groups also go through.
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