Napoli joined the Reds in the knockout stage after what may have been Carlo Ancelotti's last match in charge of the Partenopei. Much-maligned striker Arkadiusz Milik scored a hat-trick en route to a 4-0 victory over Genk that ended Napoli's winless streak at nine games.
Salzburg, who surprised the field with 16 goals in the group stage, finished in third and now drops into the second-tier Europa League. Genk could only manage a point in fourth.
Liverpool were under swaths of pressure in the first half of Tuesday's match, and if not for Alisson's double save in the seventh minute, their chances of progressing would've taken a massive hit. There was no mistaking Salzburg's urgency - they had to beat Liverpool by at least two goals to muscle the defending champions out of a qualification berth.
Not that Liverpool were rolling over. Mohamed Salah continuously found himself in scoring positions and missed a glorious chance in the 29th minute, sweeping Naby Keita's perfect pass wide of the net.
Salah burst free at the start of the second half, but Salzburg goalkeeper Cican Stankovic swatted the ball away from the Egyptian's feet.
Liverpool eventually broke the deadlock in the 57th minute as Keita headed in Sadio Mane's hopeful cross. Salah then sealed the game by converting the most difficult of his nine shots toward goal, curling the ball in from a wide and acute angle.
Napoli produced an impressive result of their own under a cloud of speculation. Reports in Italy suggest Ancelotti could leave the club, but Tuesday served as a welcomed reprieve for a team in turmoil.
Genk's Maarten Vandevoordt, who became the youngest goalkeeper in Champions League history at 17 years and 287 days, gave Napoli some help. Vandevoordt was at fault for his opponent's first goal and later conceded a penalty for bringing down Jose Callejon.