Manchester City's two-goal success over Everton in the early start had moved the reigning champions to the summit, but Jurgen Klopp's side navigated their way through a tough game with Burnley to secure the win which has taken them back to first position.
Burnley started well at Anfield, with the Clarets showing a willingness to commit players forward, and Josh Brownhill was the player setting the tone with some bright runs in the final third of the field.
Trent Alexander-Arnold found Darwin Nunez in a dangerous position in the 10th minute, with Liverpool looking to carve out an opening, but the striker just could not get his shot away.
Alexander-Arnold then struck over the crossbar in the 12th minute, before Curtis Jones missed the target three minutes later, with the home side starting to make their mark.
The breakthrough came in the 31st minute of the match through Diogo Jota, with the Portugal international having the simple task of heading into an empty net after Burnley goalkeeper James Trafford failed to clear.
Liverpool came close to scoring a second in the 43rd minute through Luis Diaz, but Trafford was on hand to make the save.
Burnley then levelled the scores shortly before the interval, with a brilliant header from Dara O'Shea silencing the Anfield crowd, and it was 1-1 at the half-time break.
Jota headed straight at Trafford in the opening chance of the second period, and there was a nervousness inside the stadium, with the visitors more than matching their opponents for long spells.
Liverpool managed to take the lead in the 52nd minute of the clash through Diaz, though, with the forward heading a delivery from Harvey Elliott into the back of the net, and it was given following a lengthy VAR check.
Jota placed a volley wide in the period that followed, with Klopp's side firmly on the front foot and seeking a third goal at Anfield.
Burnley were having chances, though, with David Datro Fofana seeing an attempt saved by Liverpool goalkeeper Caoimhin Kelleher, before Wilson Odobert missed the target from the rebound.
Fofana then curled one wide of the far post during a strong spell for the Clarets, before Jarell Quansah fired just wide for Liverpool down the other end of the field, with the final 15 minutes of the game approaching.
Liverpool made sure of the points in the 79th minute, though, with Nunez heading a cross from Elliott into the back of the net, and there was to be no further response from Burnley, who remain 19th in the table, now level on points with basement side Sheffield United.
Nunez had another couple of chances late on, but he missed the target with a header before being denied by Trafford, with Liverpool ultimately declaring at three on the afternoon.