Liverpool knew ahead of the game that they needed either a 1-0 win or, if the visitors scored, a victory by two clear goals to progress from Group C.
With the Reds starting the night in third, the Anfield crowd rallied behind them as they pushed their side to a tense but ultimately satisfying victory over Carlo Ancelotti's side.
Both sides had their fair share of chances, however it was Mohamed Salah's finish through David Ospina's legs in the first-half that saw Liverpool clinch the all-important three points.
Salah shrugged off Mario Rui to come up against Kalidou Koulibaly, who he stood up before taking the ball past him to slot home at the Anfield Road end.
It proved to be enough - thanks to a late save by Alisson - who kept out Arkadiusz Milik's close-range shot in stoppage time to keep Liverpool's Champions League hopes alive.
The Reds finished second in the group behind Paris Saint-Germain, with the last 16 draw taking place on Monday, December 17.
Slide through our gallery below for the best photos from the night...