In a turbulent match, VAR netted two Senegalese penalties, with Burkinabé goalkeeper Hervé Koffi picking up the injury in the events of the first.
Abdou Diallo and Idrissa Gueye put Senegal in charge before Blati Toure closed the gap late.
It was Mane’s 29th goal for his country, putting him level with Henri Camara at the top of their all-time goalscoring list.
“It shows you the momentum we have,” Mane said. “We knew it was not going to be easy at all to get to two consecutive AFCON finals, but the most important thing for us now is to go all the way and win, no matter who we face.
“We were up against a very good Burkinabe team which caused us a lot of problems.
“We expected a tough game and it was, but we stayed calm and created plenty of chances. I think we deserved to win.
“I think you can see on my face how happy I am, which is completely normal. I’m really proud personally and very happy for myself, my team-mates and the country.”
Just four minutes into the game at the Ahmadou Ahidjo stadium in Cameroon’s capital, Yaoundé, there was a serious clash of headers after a fully committed 50–50 challenge between Nampalys Mendy and Cyrille Bayala.
It set the tone for what would be a bloody and fiercely contested last four clash between two teams who have both reached the final of this competition in the past but never won it.
Senegal are Africa’s highest ranked team — 20th on Fifa’s world list — and their extra class has finally been revealed.
They were teased with the opportunity to open the scoring twice before the break, with Koffi’s aerial clash with Cheikhou Kouyate and Edmond Tapsoba’s elbow block on Idrissa Gueye both ruled as on-field penalties .
But both were properly knocked down by referee Bamlak Tessema Weyesa after being called to view them on the monitor by the video officials.
There was still a cost for Burkina Faso, with Koffi injured in the 36th minute after landing awkwardly on Crystal Palace midfielder Kouyate as he tried to clear.
The Stallions are used to dealing with adversity, however, having come this far despite being outsiders and against the backdrop of a military coup in their home country.
The fact that they pushed the contest so deep is a tribute to their courage and a defiant performance that gave the favorites more of a scare, mainly via Bertrand Traore’s direct run from Aston Villa.
After Idrissa Gueye entered to make it 2–0 in the 76th minute — six minutes after Diallo arrived from a corner — Kamou Malo’s team could have withered.
But Toure gave them brief hope with his 82nd-minute effort, before Senegalese talisman Mane had his say on the occasion with a driving run and a chipped finish three minutes from time.
Former Nigeria striker Efan Ekoku, speaking to BBC Three:
Sadio Mane plays like an 18, 19 year old all the time. He has a real desire.
He has real selflessness and when he plays for his country there is no ego at all.
He is one of my all time favorite players in world football, I can’t think of anyone else I would want in my team.