The Reds headed into the game looking to make it 12 wins from 13 in the top flight and on the back of their 3-1 victory over Manchester City before the international break.
Sadio Mane gave the visitors the lead in the 49th minute at Selhurst Park with his 10th goal of the season.
However, the home side looked to have earned a point when Wilfried Zaha netted in the 82nd minute to equalise for the Eagles.
But it was Liverpool FC who had the final say, with Roberto Firmino scoring the all-important winner in the 85th minute as they claimed all three points to maintain their place at the top of the Premier League table.
England legend Lineker was clearly impressed by Liverpool FC’s fighting spirit as they claimed all three points to underline their status as title favourites.
Lineker wrote on Twitter after Firmino’s equaliser: “Scruffiest of goals from Firmino makes it 2-1. This @LFC side certainly find a way to win.”
Liverpool FC are aiming to win the Premier League title this season after having finished second behind Manchester City last term.
They will take on Napoli at home in the Champions League on Wednesday night, before preparing for their next Premier League game – a home clash against Brighton and Hove Albion next weekend.
The Reds are yet to lose a game in the Premier League and have only dropped two points so far this season.
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