Missing Adam Lallana, Nathaniel Clyne and Philippe Coutinho through injury, Liverpool had precious little to really cheer until Mane struck to defeat a determined Palace side.
His 73rd-minute goal secured Liverpool’s first win of the campaign after Jurgen Klopp’s side drew 3-3 at Watford in their opening fixture.
Once again, the pre-match build-up for Liverpool had focused on the future of Coutinho in light of Barcelona’s repeated efforts to lure him to Camp Nou.
Liverpool have rejected three attempts to sign the 25-year-old Brazilian, who signed a five-year contract in January, and the club’s owners remain adamant he will not leave Merseyside any time soon.
There was better news for the home side as Daniel Sturridge returned to the team for this encounter after missing Liverpool’s first two games of the season with a thigh injury.
He was one of five alterations from the draw at Watford as Klopp looked to solidify his defence, making three changes at the back.
Frank de Boer’s Palace team lost 3-0 at home to Premier League new boys Huddersfield Town in their season opener and that result was further marred by an injury to Wilfried Zaha.
Yet despite Palace’s poor showing last weekend, they went to Anfield with hope of becoming the first team to win four consecutive matches at the ground since Arsenal managed the feat 82 years ago.
With Liverpool beginning the contest as if they meant business, that looked a forlorn hope.
Andy Robertson, making his Liverpool debut, immediately threatened for the home side, delivering a decent cross that just lacked somebody clinical enough to finish it off.
– Benteke blazes over –
Joel Matip went close to opening the scoring, but he could not quite direct Robertson’s cross goalwards after outjumping Palace goalkeeper Wayne Hennessey.
Just before half-time Roberto Firmino hit a fine effort that Hennessey did brilliantly well to keep out before Jason Puncheon did the same at the other end, rifling in an effort that Simon Mignolet punched away.
Liverpool were sharper than the opposition after the interval, but Klopp’s side still toiled to break down their stubborn visitors, Sturridge seeing one long-range attempt well saved by Hennessey.
Palace should have scored after 55 minutes as Patrick Van Aanholt did superbly to dart down the wing and into the box.
But after laying the ball back perfectly for Christian Benteke, he saw the former Liverpool striker blaze over the bar from less than eight yards out.
Star signing Mohamed Salah had started on the bench for Liverpool, but he joined the fray after an hour.
A foray into the box by Mane resulted in a chance for Georginio Wijnaldum, but he fluffed a shot from eight yards out, much to the Kop’s audible frustration.
However, Mane then made the difference with 17 minutes to go as Palace’s resistance finally crumbled.
He picked the ball up on the left wing and exchanged passes with Robertson before Palace defender Luka Milivojevic had a nightmare.
The Serbian midfielder’s stumble sent the ball into Mane’s path and the former Southampton flier slotted home.
The goal meant Palace had to come out and attack more, but apart from one Sullay Kaikai blast that was palmed clear by Mignolet, Liverpool were untroubled.