The first leg of the tie had ended in a goalless stalemate at Anfield and Jurgen Klopp's men would need something special to go past the German champions at the Allianz Arena, and that was exactly what they did, with their current best player, Mane opening the scoring before wrapping up the victory.
In the 26th minute, the Senegal international grabbed the curtain raiser in exciting fashion. After being found by a Virgil van Dijk pass at the edge of Bayern area, he showed great composure to turn away from Niklas Sule and the onrushing Manuel Neuer before dinking the ball into the far corner.
Both teams went into the break levelled after Joel Matip converted a teasing Serge Gnabry cross past Alisson. But Liverpool regained the lead in the 69th minute after Van Dijk met a James Milner corner-kick delivery with a powerful header.
Mane then took the game beyond their hosts after meeting Mohamed Salah’s sublime outside-of-the-boot cross with a diving header.
The former Southampton man's showing was enough to secure Liverpool passage to the last-eight of Europe's elite club competition on a 3-1 aggregate win.
His showing in Germany comes only three days after he became the 56th player to score 50 goals for Liverpool with his brace in their 4-1 win over Burnley, thus, increasing his tally for the club to 52.
Overall this season, he has netted 19 times, including three strikes in the Champions League and will hope to continue the impressive run when they face Fulham in a Premier League clash on Sunday.