The club’s reigning Player of the Season has made, as per his stylistic make-up, a quick dart to retaining that honour in 2017-18 by forcing matters when the Reds find themselves stuck in a stagnant possession loop.
They spent most of their first Anfield outing of the campaign commanding an average of 70 per cent of the ball against Crystal Palace, but once again were sans guile and inventiveness in midfield.
And so, as proceedings on Saturday afternoon seemed to be fading into nothingness, it was left to the Senegal international to remind Liverpool of their ‘simple and quick’ mantra.
The goal had a sprinkling of fortune about it, but - in one of Jurgen Klopp’s repeated messages - you breed your own luck when you’re not passive.
It came on 73 minutes with Joel Matip feeding James Milner, stationed on the left of midfield, who then passed to Mane on that flank.
Tight on the byline, Palace were comfortable enough to feel there was no threat on. But the 25-year-old stood up Joel Ward, engaged in a fast one-two with Andy Robertson, and continued to speed goalwards even though it looked as though the move had broken down.
Luka Milivojevic picked up the loose ball, but under pressure from Dominic Solanke, who had only been on the pitch for two minutes, ceded it and Mane was alert to the opportunity, happily striking past Wayne Hennessey into the bottom-left corner.
That finish - the forward's sixth league goal in the last eight matches - ensured Palace would not become the first side to win four top-flight games on the spin at Anfield since Arsenal in December 1935.
Mane sprinted straight to Klopp in scenes reminiscent of Liverpool’s 4-3 opener against Arsenal at the Emirates last year, but there was no piggy back and mass celebration this time around.
In the huddle on the touchline, though, the manager did show his appreciation for Solanke’s contribution in the build-up.
"I thought it was a wonderful goal," the 50-year-old said. "It was not the best one-two but Dom stayed awake and put the foot in.
"It was counter-pressing, I love it. Sadio was alone and could score – well deserved, not perfect but well deserved."
Another player that impressed the German was Andy Robertson. Having been excluded from the first two matchday squads, he was Liverpool’s creator-in-chief on his competitive debut for the club.
The left-back’s deliveries - inviting and varied - did not get the treatment they deserved in the first half, when he constructed three clear-cut chances for Milner, Matip and Mane.
Signed from Hull City for an initial £8 million this summer, the 23-year-old was the pick of Klopp’s XI during the opening spell and continued to be lively in the second half.
"I think everybody could see how good Robbo, especially in the offensive situations, can be with a few more sessions," Klopp explained.
"His crosses are a real threat. When you think a little bit about how you would feel if you were playing your first game at Anfield - you cannot be full of joy, there’s a lot of pressure on yourself and he did really well."
Despite the result, the performance still fell far short of the fluid, assertive and exhilarating showing expected from the Merseysiders.
It was yet another fixture - number three of three - in which the club’s unrelenting stance that Philippe Coutinho is not for sale at any price this summer made complete sense.
In his absence through a back injury as he attempts to force through a transfer to Barcelona, Liverpool do not possess an experienced playmaker capable of properly servicing their formidable frontline, especially with Adam Lallana sidelined.
"Football playing in the first half could have been better, 100 per cent," admitted Klopp.
"I’m really happy that we scored and we created chances in the second half. First half… offensive football, like always, is about making the right decision in the right moment.
"It’s about timing and we didn’t see the spaces in the first half often enough, but we could show the players at half-time where the spaces are – one little pass, one switch and the world is much nicer. We didn’t do this often enough, we stuck in this area, looking there and forgetting the rest of the pitch. That was the problem.
"We didn’t play too often with these three [midfield] players together. Millie did outstandingly good again but needs to adapt again of course, it’s a different role to last year.
"We had nobody in the box from this position. If there’s no-one in the box you cannot score."