Liverpool overcame a poor referee decision in the first ten minutes of the game to turn the game around within the first half.
Adam Lallana rewarded the Liverpool boss for his inclusion in the first team with a solid first half performance - he was instrumental in the reds first two goals.
The reds move back to within one point of leaders Man City with a huge cushion ahead of third placed Spurs.
Jurgen Klopp brought back Roberto Firmino to the starting line up, in place of Divock Origi. But a bit of a surprise in midfield - with Adam Lallana in for Jordan Henderson.
In the pre-match build up Klopp insisted that across the five training sessions this week that Adam Lallana looked exceptional and thus justified his position in the team.
And it turned out to be an excellent managerial decision.
The weather was strange at Anfield especially in the first half, sunshine, then sleet, then hail, then strong winds but the strangest thing was the opening goal.
From a corner Ashley Westwood fired it straight into the net. But Alisson was furious and ran to the referee.
Replays showed that James Tarkowski was all over the Brazilian keeper - preventing him from moving. A clear foul missed by the ref. And to add insult to injury Alisson was handed a yellow card for his appeals.
Coming the day after Raheem Sterling broke the deadlock for Man City with an offside goal it would have been easy for Liverpool's heads to go down.
But they fought back decisively.
In the 19th minute Roberto Firmino got the equaliser. Lallana sending in a cross that Salah picked up on the touchline. The Egyptian worked the ball across the face of goal - Tarkowski got the meekest of touches on it and Firmino had the simplest of tap ins.
Ten minutes later and Sadio Mane gave Liverpool the lead. Lallana intercepting the ball with a sliding tackle it fell to the Egyptian who steered it into the path of Mane who curled in to the goal.
Mane has now scored in six consecutive league games at Anfield.
Burnley started the second half a bit brighter, with the winds at their back. Virgil van Dijk was forced to react quickly to a wind assisted pass that could have caused problems within the first five minutes.
As the half wore on however Liverpool exerted their control and it was no surprise when the reds added a third goal.
Tom Heaton, another England international goalkeeper, firing a goal kick straight out to Mo Salah who ran towards goal. A challenge came in but the ball headed in Firmino's direction. Another tap in for the Brazilian.
And then two goals in injury time. Firstly Burnley grabbing one back in the 91st minute when substitute Berg Gudmundsson sent the ball tumbling past the Liverpool keeper after a defensive switch-off.
Would it be a nervy end to the game?
Not likely, after Sadio Mane reacted quickest in the final seconds of the game to round the keeper and fire into the Kop net. A deserved second goal of the game for the talented reds forward.
Liverpool move on to 73 points after 30 games, equalling that 1987/88 record LFC team and are back to one point behind Man City.
The gap to third placed Spurs is now an astonishing 12 points, just weeks after pundits were suggesting that Spurs should not be ruled out of a title race.
There are only two teams in it now, and Liverpool and Man City have eight games to go.