Mane needed less than 10 minutes to open the scoring in the Stadio Olimpico, as Liverpool's bid to defend the 5-2 lead picked up in the first leg got off to a perfect start.
After Radja Nainggolan's horrendous pass was picked up, the striker was fed in by Roberto Firmino and finished in emphatic fashion past Alisson.
The goal put Liverpool 6-2 ahead on aggregate, with Georginio Wijnaldum later restoring the four-goal advantage following James Milner's own goal.
The trio of Mane, Mohamed Salah and Firmino have now hit no less than 29 goals in this year's Champions League.
Salah and Firmino have contributed 10 each, with Mane chipping in with nine more.
That is more than any other forward trident has ever managed in a single campaign, breaking the record previously held by Cristiano Ronaldo, Gareth Bale and Karim Benzema that was set in 2013-14.
29 - Mo Salah (10), Roberto Firmino (10) and Sadio Mane (9) are now the highest scoring trio for a club in a single #UCL campaign, overtaking Ronaldo, Bale and Benzema at Real Madrid in 2013-14 (28). Ménage.— OptaJoe (@OptaJoe) 2 de mayo de 2018
The strike also means that Mane has scored nine times in his first 10 Champions League appearances - a new record.
Mane now passes Harry Kane and Simone Inzaghi as the most proficient novices in Europe's most important club competition.