The first-leg tie of round of 16 played in Germany last month and it was ended goalless, with Riyad Mahrez and Josko Gvardiol scored for their respectively teams.
However, second-leg tie hold at Etihad stadium this evening, and Pep Guardiola's side thrashed the Bundesliga side with high figures of goals.
Manchester City made perfect start to the game and found themselves lead inside 21 minute through inform striker Erling Haaland.
The centre-forward scored from spot-kick to put City ahead. Two minute later he doubled his side's lead with a tap-in.
Haaland ended the first opening 45 minute with hat-trick after scored third goals towards the end of half-time.
Early in second-half, Ilkay Gundogan produced remarkable strike to extend the City lead before Haaland bagged two more goals to make it 6-0.
Five sensational goals against RB Leipzig means Erling Haaland has become second players in history to scored five goals against opponents after Lionel Messi.