Roberto Firmino and Sadio Mane both scored twice as Liverpool recovered from conceding a controversial opener to beat Burnley 4-2 and close the gap on Premier League leaders Manchester City to one point.
Burnley took the lead in the sixth minute when Ashley Westwood scored direct from a corner, with the ball flying over goalkeeper Alisson, who appeared to be impeded on the line.
Liverpool responded as Firmino scored from close range in the 19th minute and then Mane curled in with a fine first-time finish.
Liverpool: Alisson (6), Alexander-Arnold (6), Van Dijk (7), Matip (6), Robertson (7), Fabinho (7), Wijnaldum (7), Lallana (7), Mane (8), Salah (6), Firmino (8)
Subs: Henderson (5), Keita (5), Sturridge (5)
Burnley: Heaton (5), Taylor (6), Mee (5), Tarkowski (5), Bardsley (6), Westwood (7), Cork (6), McNeil (7), Hendrick (5), Barnes (5), Wood (5)
Subs: Crouch (5), Gudmundsson (6), Vydra (5)
Man of the match: Sadio Mane
Blustery conditions made it difficult for both sides but Firmino's second goal in the 67th minute gave the hosts breathing space.
Johann Berg Gudmundsson set up a nervy finish when he struck in injury-time, but Mane replied to make sure of victory.
Aside from the final couple of minutes and the opening spell after Westwood's goal, Liverpool were largely in control as they closed the gap on City, who beat Watford on Saturday to move four points clear.
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Both sides now have eight games left to play as they battle for the title, while Burnley are two points above the relegation zone after a third loss in a row.
Burnley took the lead in controversial circumstances as Westwood scored direct from a corner in the sixth minute.
Liverpool were furious the goal was allowed to stand as goalkeeper Alisson appeared to be impeded from getting near the ball by two Burnley players.
However, the home side responded in the 19th minute when Tom Heaton and James Tarkowski both missed Mohamed Salah's cross, giving Firmino a tap-in from a few yards out.
Mane then curled in with a fine first-time finish from inside the box to put Liverpool ahead.
With rain, sleet and wind making conditions difficult, there were no further chances before half-time and it remained closely-fought after the break.
However, Liverpool scored their third when Heaton's clearance went straight to Salah and, although he was well tackled by Charlie Taylor, the ball fell to Firmino to finish into an empty net.
Mane missed a glorious chance to make it 4-2 when he slid in and turned a cross onto the bar from a few yards out.
Burnley had hardly threatened in the second half, but Gudmundsson struck in injury-time to set up a nervy couple of minutes.
Firmino and Lallana started for Liverpool in place of Origi and Henderson. Burnley stuck with the same XI that lost to Crystal Palace last time out.
However, Liverpool hit back with a fourth goal as Daniel Sturridge played through Mane and he rounded Heaton and tapped in.
- Liverpool's tally of 73 points from their opening 30 league games this season is their joint-best ever total at this stage of a league campaign (adjusting to three points for a win), level with the 1904-05 second tier season and 1987-88 in the top-flight.
- Liverpool are the first side to win four consecutive home Premier League games in which they conceded the first goal since Chelsea won six in a row between April 2013 and May 2015.
- Burnley have dropped more points from winning positions in their 30 Premier League games this season (10) than they did in the whole of 2017-18 (nine).
- Liverpool have now gone 36 Premier League games without a loss at Anfield (W26 D10), the joint-third longest unbeaten home run in the competition's history, behind only Chelsea (86 games between March 2004-October 2008) and Manchester City (37 between December 2010-December 2012).
- Liverpool have conceded nine goals in their 10 Premier League games in 2019, one more than they had in their 20 league games this season before the turn of the year.
- Roberto Firmino has now scored 10+ goals in all four of his Premier League seasons with Liverpool, the best 100 per cent record of reaching double figures of any player for the club in the competition.
- Roberto Firmino has been directly involved in 100 goals in 175 appearances in all competitions for Liverpool under Jurgen Klopp (63 goals, 37 assists), more than any other player in that time.
- Ashley Westwood has scored his first Premier League goal for Burnley, and his first overall since April 2016 when he scored twice for Aston Villa against Southampton, 1051 days ago.
Man of the match - Sadio Mane
As he has been over the last couple of months, Mane was again the star man for Liverpool. He looked bright throughout and produced a fine curling finish to put Liverpool ahead. He then scored again in injury-time, making amends for a glaring miss, and has now scored 50 goals for Liverpool in all competitions in 109 appearances.
He is also the fifth Liverpool player to score in six consecutive home appearances in the Premier League, after Michael Owen, Fernando Torres, Luis Suarez and Mohamed Salah.
Liverpool travel to Bayern Munich on Wednesday for the second leg of their Champions League last-16 clash with the tie goalless. They then face Fulham next Sunday, live on Sky Sports.
Burnley host Leicester in the Premier League on Saturday.