The Reds led 3-2 as the final whistle of a topsy-turvy match approached, but after James Milner was sent off in the 89th minute for two yellow-card offences, it was a nervy ending as the Premier League leaders desperately tried to hold on to their lead.

The win was ultimately secured when Sadio Mane added a fourth in stoppage time, though there was still time for Max Meyer to score a consolation for the visitors.

Liverpool had dominated the vast majority of the first half at Anfield but it was Palace who broke the deadlock through Andros Townsend, who beat Alisson from close range after Wilfried Zaha pulled a cross back.

The hosts came out for the second period with goals on the agenda, and it took just one minute for Salah to equalise before they went ahead seven minutes later through Roberto Firmino.

Palace were not down and out just yet, though, and James Tomkins capitalised on poor defending to head his side level from a corner.

However, a calamitous error by Julian Speroni - making his first appearance since December 2017 - handed Liverpool an advantage they did not relinquish again, the visitors' keeper scooping the ball towards his own net for Salah to poke in from on the line.

With the rest of the top four yet to play this weekend, Liverpool remain seven points clear at the top of the table, while Crystal Palace stay 14th.

Liverpool battle through

It was a tense performance from start to finish on a day Liverpool were paying tribute to Bob Paisley, the club's most successful manager, before what would have been his 100th birthday on Wednesday.

Prior to Saturday's game, Liverpool had conceded just three goals at home all season, but that was soon to change as Roy Hodgson's Palace rolled into town.

Making his first start for the Reds since 11 December, Joel Matip had two early chances to open the scoring but Jurgen Klopp's side struggled to find a response after Townsend's goal.

Whatever Klopp said to his players in the dressing room at half-time worked, though, with Salah bringing his side level with a toe poke after Virgil van Dijk's long-range effort had deflected into his path off James McArthur.

It was a goal that lifted the atmosphere at Anfield as Liverpool capitalised on the change of tempo, Firmino making no mistake with his right foot to put the Reds ahead.

Sloppy defending at a corner allowed Tomkins to equalise but Speroni soon gifted Liverpool the winner with a mistake he will not forget in a hurry, Salah tapping home from on the goalline for his half-century of top-flight strikes.

Three points were secured when Mane scored a simple goal, after Milner had been dismissed for two mistimed challenges on Zaha.

Liverpool have now won seven consecutive Premier League home games for the first time since January 2014, and extend their unbeaten league run at Anfield to 32 matches.

Palace give Reds a run for their money

The Eagles have impressed against the Premier League's big guns this season, most notably their 3-2 win over second-placed Manchester City in December, and it looked as though they could pull off a repeat of that Etihad Stadium victory as they refused to allow Liverpool to play the football they wanted.

Never before had a Hodgson side conceded a goal against the Reds at Anfield and their opener, which was against the run of play, shocked Liverpool into silence and sent them into the break with the advantage.

Luck was on their side as their hosts struggled to supply the final pass. Even after Liverpool went ahead, Zaha and Patrick van Aanholt continued to be a nuisance for their defence and Tomkins' goal was a just reward for their resilience.

Hodgson made three substitutions in quick succession as Palace searched for an equaliser after Salah's second, with one of them, Jeffrey Schlupp, going close from a Van Aanholt free-kick.

Liverpool last conceded three goals at home in the league almost exactly a year ago when they beat Manchester City 4-3

Even Meyer's late strike - his first in a Palace shirt - proved not to be enough as Liverpool continued their journey towards the title despite conceding three at home in the league for the first time since a 4-3 win over Manchester City on 14 January 2018.

Man of the match - Jordan Henderson (Liverpool)

Liverpool captain Jordan Henderson can sometimes go without credit, but he stayed calm when his side were under pressure with exceptional passing to create chances for his team

Liverpool bring up their 1,000 - match stats

• Crystal Palace are the first Premier League team to score more than once at Anfield since February 2018, when Tottenham drew 2-2 with Liverpool.
• Liverpool hit the 1,000 goal mark in home games in the Premier League, becoming only the third side to do so after Manchester United and Chelsea.
• Crystal Palace keeper Julian Speroni (39 years 246 days) became the oldest player to make a Premier League appearance this season, and the oldest to appear in the competition since Shay Given (40 years 151 days) in September 2016.
• Wilfried Zaha's assist for Palace's opener was his first goal involvement in his past 14 league games.
• Palace's Andros Townsend scored his fourth league goal of the season, equalling his best in a Premier League campaign (also four in 2015-16).
• Liverpool's Mohamed Salah scored his 50th Premier League goal in his 72nd appearance in the competition - only Andrew Cole (65), Alan Shearer (66) and Ruud van Nistelrooy (68) have reached the milestone in fewer appearances.
• Since Jurgen Klopp took over at Liverpool in October 2015, Roberto Firmino has been directly involved in 69 Premier League goals, more than any other player for the Reds (45 goals, 24 assists).
• James Milner picked up his second red card for Liverpool in the league. He was also sent off against Crystal Palace in March 2016 after fouling Wilfried Zaha.
• Liverpool's Sadio Mane has scored in his past four Premier League games against Palace, the first time he has netted four in a row against one opponent in the competition.

What's next?

Next weekend sees the FA Cup return so Liverpool, having been knocked out in the third round, now have a 10-day break before hosting Leicester in the league on Wednesday, 30 January (20:00 GMT kick-off).

Palace host Premier League rivals Tottenham in the FA Cup next Sunday (16:00) before travelling to Southampton in the league on 30 January (19:45).