- Jurgen Klopp's side were looking to respond after last weekend's defeat by Arsenal, and having fallen a point behind Manchester City.
- They took the lead through Diogo Jota's header from a corner which Burnley keeper James Trafford failed to claim.
Image: HANDOUT
Liverpool returned to the top of the table as they got back to winning ways against struggling Burnley in front of a club record league crowd at Anfield.
Jurgen Klopp's side were looking to respond after last weekend's defeat by Arsenal, and having fallen a point behind Manchester City.
They took the lead through Diogo Jota's header from a corner which Burnley keeper James Trafford failed to claim.
The Clarets, who have been in the relegation zone for most of the season, levelled before half-time through Dara O'Shea's superb header before Luis Diaz restored the lead in the 52nd minute.
Burnley had several chances to equalise before Darwin Nunez's header from Harvey Elliott's cross sealed the points.
On a tetchy afternoon, both Liverpool manager Jurgen Klopp and Burnley boss Vincent Kompany were booked by referee Tim Robinson for protesting after decisions went against their teams.
Liverpool were without first-choice keeper Alisson because of illness but stand-in Caoimhin Kelleher made a fine save to deny David Datro Fofana an equaliser when the score was 2-1.
The Reds, watched by a crowd of 59,896, had briefly been replaced at the top of the table after City's 2-0 win over Everton in the early kick-off.
But Liverpool reclaimed their two-point advantage - albeit having played one game more than their nearest rivals - while Burnley remain 19th.
Relief for Reds
This was not a straightforward win for Liverpool, who were once again far from their best following the setback against Arsenal.
There was relief at the final whistle after Burnley, who have won just three league games all season, squandered some fine opportunities to score, while Kelleher came to the rescue to keep out Fofana after half-time.
It was only after Nunez's header in the 79th minute that the Reds were able to relax after numerous scares.
Liverpool, who were also without Joe Gomez through illness, have been good at grinding out results without playing particularly well this season and their latest performance certainly fell into that category.
But it is results that count at this stage of the season - and the Reds still have Mohamad Salah to return from a hamstring injury, although they have coped in the absence of their leading scorer.
This was their sixth win in eight games in all competitions since Salah last played for the club, and they have scored 22 times in that period.
Another positive for Klopp was a first start for four months for full-back Andy Robertson after injury but there was concern after Trent Alexander-Arnold's game was cut short by a knee problem.
"It's nothing really bad but he felt it again and we have to see," Klopp said.
"We were made aware of it in the game so I thought 'what can we do?' then Trent said 'no, it's fine'. But it's not as he feels it so we had to be careful and take him off."
Clarets show spirit but future looks bleak
Burnley's hopes of avoiding relegation look decidedly bleak following a 17th league defeat.
The club that finished on 101 points in the Championship last season are seven points from safety, with Arsenal to come next weekend.
Clarets boss Kompany, a four-time Premier League winner, never won at Anfield in eight visits with Manchester City and he once again left empty-handed despite seeing his players carve out nine attempts, four of which were on target.
Fofana, starting for the first time since joining on loan from Chelsea, put a good chance wide having earlier been denied by Kelleher.
There were positives for Kompany as Burnley started well, and responded through O'Shea's header after falling behind.
But the worry for the Clarets is that they have now conceded 50 goals and are without a win in five Premier League games.