However, the Premier League leaders must now avoid defeat to Red Bull Salzburg in two weeks' time in order to guarantee a top-two position in Group E, with Napoli able to progress with victory over Genk.
Liverpool, who were eager to avoid a last-match decider given their upcoming hectic schedule, went into the contest aware that they required a much improved performance after losing to Napoli on matchday one.
However, for all of their possession, Jurgen Klopp's team barely offered a threat during the opening stages, while the home side were also dealt an early blow as Fabinho was forced off with an ankle injury.
The first quarter of the match got worse for Liverpool as Napoli took the lead in controversial circumstances. Mertens appeared to foul Virgil van Dijk on the halfway line, but play continued before the Belgian eventually broke clear to fire a shot into the far corner of Alisson's net from 10 yards.
Despite a prolonged VAR check which also included numerous replays regarding an offside check, the goal was allowed to stand, much to the frustration of Van Dijk, who required several minutes of treatment.
Nine minutes before the half-time whistle, Van Dijk saw a tame header easily saved by Alex Meret, and that was as good as it got for Liverpool heading into four minutes of added-on time.
While James Milner engineered an opportunity for himself down the left-hand side of the area before forcing a save out of the Italian stopper, it did not stop Klopp from sprinting down the tunnel to work on a change of strategy for his side.
Like in the first half, Liverpool took their time to find any kind of rhythm after the restart, although they were almost gifted an equaliser by Meret.
Nevertheless, that opening acted as the catalyst for further opportunities for the hosts, with Mohamed Salah firing straight at Meret from 14 yards out and Firmino sending a header wide of the near post after meeting an Alex Oxlade-Chamberlain cross.
However, the equaliser finally arrived in the 65th minute. An outswinging corner from the right found the head of Lovren, who rose above Mertens to power a header into the corner from by the penalty spot.
Klopp would have expected his team to keep up the momentum heading into the closing quarter of the contest, but Napoli were making every attempt to nullify the English outfit by dropping deeper into their own defensive third.
Liverpool's best opportunity went the way of Georginio Wijnaldum, who chested the ball down on the edge of the area before sending a volley marginally wide of the top corner.
However, for all of their pressure, Liverpool could not create anything of note in the closing minutes, meaning that they must avoid defeat in Austria on matchday six or risk an early elimination from the competition which they won in June.
LIVERPOOL (4-3-3): Alisson; Gomez (Oxlade-Chamberlain 57'), Lovren, Van Dijk, Robertson; Henderson, Fabinho (Wijnaldum 19'), Milner (Alexander-Arnold 78'); Salah, Firmino, Mane
NAPOLI (4-4-2): Meret; Maksimovic, Manolas, Koulibaly, Rui; Di Lorenzo, Allan, Ruiz, Zielinski (Younes 85'); Lozano (Llorente 72'), Mertens (Elmas 81')body check tags ::