For a moment the Clarets had threatened to put their stamp on an unusual collection of results at the bottom end of the Premier League over the weekend.
Cardiff City plugged the gap on the Clarets to just two points with victory over West Ham United while Southampton, Brighton, Newcastle United and AFC Bournemouth all picked up three points to strengthen their respective causes.
Burnley had led at Anfield for the third season in succession when Ashley Westwood scored his first goal in almost three years.
The midfielder's corner, conceded by Fabinho, floated all the way in at the far post after James Tarkowski had applied the pressure on goalkeeper Alisson.
It was the first goal that Sean Dyche's side had netted from outside the penalty area in the top flight since Steven Defour's free kick against Manchester United at Old Trafford last term. They'd scored 50 goals in-between.
Westwood's opener, his first goal since his brace for Aston Villa in a 4-2 home defeat to Southampton, was only the third time that the Reds had trailed in the league at Anfield this season.
And it temporarily troubled their title aspirations. However, it wasn't long until Jurgen Klopp's side swung the game in their favour.
Roberto Firmino had asked questions of the Burnley defence when space had opened up for him from Mo Salah's pass, only for Tarkowski to deflect the attempt over the bar.
But the Brazilian forward had the hosts back on level terms moments later, capitalising on a mix up at the back between Tom Heaton and Tarkowski.
The pair failed to deal with Salah's ball across the six-yard box, after the Egyptian forward had switched passes with Georginio Wijnaldum, and Firmino tapped home in to an empty net.
The visitors were then the masters of their own downfall for Liverpool's second just before the half-hour.
Adam Lallana blocked Phil Bardsley's attempted clearance, following a moment of hesitancy from the full back and Jeff Hendrick, and when the ball broke from Charlie Taylor's challenge on Salah, it was Sadio Mane who fired in to the corner.
Another defensive error saw Salah shoot wide of the near post afterwards but Burnley were still in the game at the break.
In Burnley's search for an equaliser, the home side were always going to be dangerous when exploiting the extra pockets of space.
And so it proved. Salah shaved the outside of the upright with an effort from outside the box while Firmino went just as close with a deceptive attempt that span just wide once Mane had broke through the middle.
It was frustrating, though, that the title contenders didn't have to work for their third goal, either.
Salah couldn't believe his luck when Heaton's kick landed straight at his feet and even though the 26-year-old was dispossessed by Taylor inside the box, Firmino followed up to make it 3-1.
Mane should have opened up a three-goal cushion when throwing himself at Trent Alexander-Arnold's cross late on but the Senegalese striker somehow turned the ball on to the crossbar when unchallenged from close range.
Heaton would have hoped to have done better with Liverpool's opening goals in each half, especially with the England squad announcement imminent, but he did well to prevent Salah inflicting further damage on the away side.
The Three Lions hopeful, who last represented his country in the summer of 2017, flew over to his right hand post to turn the Golden Boot challenger's effort wide.
Dyche rang the changes in a bid to get back in to the game and he had a response when all three substitutions combined to cut the deficit.
Peter Crouch, who received rapturous applause on his return to Merseyside, won a header in the box, Matej Vydra squared the ball to Johann Berg Gudmundsson and the Icelandic international beat Alisson at his near post.
It was all set up for a grandstand finish but the Reds put the game to bed with the final kick of the afternoon.
Liverpool substitute Daniel Sturridge held the ball up well and executed a perfectly weighted pass over the top to Mane, who rounded Heaton and slid the ball in to an empty net.