Liverpool’s No.10 clipped a calm, left-foot finish over the goalkeeper in the 87th minute of Wednesday’s last-four tie to extinguish Burkina Faso’s hopes of a late fightback soon after they had pulled a goal back.
Mane had earlier provided an assist for Idrissa Gueye to put his country 2-0 up in Yaounde.
Senegal, who saw two penalties overturned following VAR reviews in the first half, dominated much of the game but had to wait until the 70th minute to take the lead through Abdou Diallo.
Soon after, Mane did brilliantly to win the ball back on the byline and unselfishly square for Gueye, who slotted home.
Burkina Faso quickly grabbed a goal to set up a potentially dramatic ending, but Mane eased his side’s nerves by racing onto Ismaila Sarr’s pass and finishing clinically.
Senegal will now face either Mohamed Salah’s Egypt or hosts Cameroon in Sunday’s final.