Liverpool had to wait until the 73rd minute to get the winner, the ball fortuitously falling to Mane inside the box after Luka Milivojevic's mistake on the edge.

Christian Benteke missed a clear opening for Palace earlier in the second half from 10 yards, blazing over the bar for the visitors' best opportunity.

Liverpool, who were without Philippe Coutinho again with his future still uncertain, held on for their first league win of the season, while Frank de Boer's new Palace side are without a point after two games.

Both sides were looking for their maiden Premier League victory of the campaign, and it was the hosts who had the best chance in a goalless first half.

The impressive Andrew Robertson, making his debut for Liverpool, sent a superb ball in from the left, but Joel Matip somehow headed wide from three yards after Wayne Hennessey had misjudged.

Roberto Firmino forced Hennessey into a fine stop from long range later in the half, before Palace went up the other end and saw Jason Puncheon's effort from an angle beaten away by Simon Mignolet.

Hennessey was at his best again in the second half, saving from Gini Wijnaldum and Jordan Henderson's long-range effort, but Palace should have been ahead on 57 minutes through former Liverpool striker Benteke, who struck over the bar after Ruben Loftus-Cheek's fine work on the right byline.

Liverpool piled on the pressure and got their reward with 17 minutes remaining as Milivojevic bolted under the pressure of sub Dominic Solanke, allowing the ball to fall luckily into the path of Mane, who made no mistake low into the net.

Solanke, Robertson and Mohamed Salah could have doubled Liverpool's lead late on, but all three were denied by Hennessey as Palace stayed in the game until the final moments.