Liverpool conceded late and early at Anfield against Burnley but still comfortably moved back to within one point of Premier League leaders Manchester City.
City had extended their lead to four points with their convincing win over Watford on Saturday so it was up to the Reds to try and keep pace.
When Ashley Westwood scored direct from a corner into the Kop end goal after just six minutes, fears that Liverpool's title jitters were about to get worse were raised.
Westwood’s effort was controversial, with replays showing goalkeeper Alisson Becker was impeded by two visiting attackers as the ball looped across the box and into his net.
But Jurgen Klopp’s men responded well and were ahead at the break thanks to goals from Roberto Firmino and Sadio Mané.
Firmino extended their lead when he made it 3-1 after 67 minutes and Liverpool really should have wrapped up the points with a string of good chances not finished, their top scorer Mo Salah particularly looking out of sorts in front of the target.
They conceded a sloppy goal to Johann Berg Gudmundsson in stoppage time at the end of the game and there were a few nervous moments before Mané made the points safe with his second of the day just before the final whistle.
Key to the win was Adam Lallana, not the most popular choice among fans to replace Jordan Henderson in midfield, who on only his fifth start of the season had a hand in the first two goals.
With high winds and occasional driving rain battering Anfield it was made for a day of potential slip-ups and there were barely six minutes gone when the setback came.
Joel Matip's poor, misdirected header gave Burnley a corner they barely deserved and they gratefully accepted that gift and the subsequent one from referee Andre Marriner.
Alisson Becker tried to leap to catch Westwood's in-swinging corner but with James Tarkowski using the Brazilian's shoulders for leverage he failed to get off the ground and the ball dropped inside the far post.
It was Westwood's first in the Premier League since scoring for Aston Villa in April 2016.
Complaints from Liverpool fell on deaf ears and to add insult to injury Alisson was booked for running 40 yards to complain to the official.
The sense of injustice was what the hosts needed to light a fire on a slow-burning midday kick-off hugely affected by buffeting high winds and sudden, torrential downpours.
Lallana started to pull the strings in midfield with Firmino, the other change from last weekend's goalless Merseyside derby, leading the forward press.
Lallana's superb crossfield ball picked out Salah, who beat his two markers and exchanged a pass with Georginio Wijnaldum with goalkeeper Tom Heaton making a mess of the cross, palming it onto Tarkowski to allow Firmino to tap home from a yard.
Liverpool's defence has been praised for conceding only 16 goals this season but they are also the first team to have three players reach double figures for Premier League goals thanks to Firmino's 10th of the campaign.
Lallana was determined to make the most of a rare start and it was his sliding block on the edge of Burnley's penalty area which forced the ball towards Mane.
Mane pounced to curl home a first-time shot to score for the sixth succession home Premier League match - a feat only achieved by Michael Owen, Fernando Torres, Luis Suarez and Mohamed Salah at Anfield.
After 67 minutes a terrible goal-kick from Heaton went straight to Salah and although he was brought down in the area play was let go on and Firmino rammed home the loose ball.
Mane should have put the finishing touches on victory but somehow hit the crossbar from three yards after Trent Alexander-Arnold's low cross with Salah, still searching for his 50th league goal for the club, denied by Heaton.
Gudmundsson struck in added time but any hope of forcing a draw were ended by Mane rounding Heaton and scoring into the empty Kop goal second later.