Fit-again Mane climbed off the bench to poke home his 12th league goal of the campaign and extend champions-elect Liverpool’s winning streak to 17 top-flight matches.
The runaway leaders inched closer to a first title since 1990 by grinding out a nervy win, amid howling winds and driving rain.
Jurgen Klopp’s men are now just one victory away from matching Manchester City’s Premier League record of 18 successive wins.
For much of a weather-ruined clash the Reds feared a first league draw since the 1-1 tie with Manchester United on October 20, only for super sub Mane to deliver in style.
The match’s sole moment of quality proved a fine way for Mane to mark his first Liverpool action since hobbling out of the Reds’ 2-1 win at Wolves on January 23.
The ever-increasing wind ruined anything remotely approaching beautiful football.
The conditions always threatened eye-catching moments for the wrong reasons, but both sides just about avoided any kind of catastrophe in an underwhelming first-half.
So much so that the Canaries had the chance of the half, but they were denied by Alisson Becker. Lukas Rupp latched on to a ball over the top and found himself one on one with Alisson, only to attempt a pass to Teemu Pukki when he should have struck on goal and the goalkeeper quickly palmed away the pass to remove the danger.
Liverpool pressed and probed for the remainder of the half but not just without success – with precious little threat.
The Reds hoped the change of ends would boost their control of the conditions, but after the interval the mediocrity continued for both teams.
A miscued Jordan Henderson pass even let Pukki cut away down the left, before the Liverpool skipper was able to head away the danger.
Salah spun away from three defenders for some rare space in the area, but Krul parried his low drive – and was then able to deny Keita on the follow-up.
Liverpool kept pressing and pressing, and Norwich somehow scrambled clear from Salah’s probing cutback.
A rare Norwich break was capped with Alex Tettey striking the base of the right post with Alisson stranded, and suddenly the Reds had to fend off the pressure of two Canaries corners.
But just when Liverpool appeared set to drop points, Mane delivered with a lovely touch to control Henderson’s ball over the top and then prod past Krul.