Mane opened the scoring with a superb goal in the 26th minute before Bayern equalised in the 39th minute due to Joel Matip’s own-goal.
However, Virgil van Dijk headed the visitors back into the lead from a corner in the second half, before Mane secured Liverpool FC’s place in the last eight with a fine finish in the 84th minute.
Liverpool FC will now await to find out their opponents in the quarter-finals when the draw is made on Friday morning.
And Manchester United legend Ferdinand was quick to praise Mane and Liverpool FC as a whole after their impressive victory over Bayern away from home.
Speaking to BT Sport after the game, Ferdinand said: “It wasn’t a great performance from this Liverpool team, we’ve seen them play better.
“But at this stage, knockout football is not about performing. It’s coming here and getting the win.
“I wouldn’t put this Bayern team up there with any of the teams that I’ve seen over the last five to eight years.
“But it doesn’t matter, they’ve still got the history, they’ve got pedigree, they’ve got talent in this team.
“This Liverpool team, they came here and it’s a great sign for them that they didn’t play particularly well but they got a fantastic result.
“Mane was the difference. What a fantastic player he has been.
“[Mohamed] Salah didn’t play particularly well but again, a moment, a game-defining moment for the third goal, a beautiful pass.
“There weren’t great performances all over the park from this Liverpool team but they found a way to get a result.
“That is a fantastic sign for this team and I’m sure Klopp will be delighted with that in that sense.”
Mane has now scored 19 goals and made one assist in all competitions for Liverpool FC so far this season.
The Reds will return to Premier League action on Sunday afternoon when they travel to Fulham in the top flight.
Liverpool FC are currently one point behind leaders and defending champions Manchester City.
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