Burnley 1, Liverpool 2
Johann Berg Gudmundsson looked to have secured a point for Burnley when cancelling out Sadio Mane's strike with two minutes of normal time remaining but defender Ragnar Klavan left it late to snatch the spoils.
The Clarets had kept 10 clean sheets in the Premier League going in to the New Year's Day fixture, with just shipped in 10 outings on home soil, and it looked as though they were heading for another with the game goalless at the interval.
It perhaps didn't help Liverpool's cause that they had to adapt to being without Mohamed Salah, Philippe Coutinho and Roberto Firmino who were all missing from Jurgen Klopp's XI.
The trio had 33 goals between them so far this season in the top flight but Salah missed out with a groin injury, Coutinho was ruled out with a thigh strain while his Brazilian compatriot was dropped to the bench.
Burnley made just one change with James Tarkowski returning from a three match suspension to replace Kevin Long at the heart of the home side's defence.
The hosts were the first to threaten when Scott Arfield closed Trent Alexander-Arnold high up the pitch and delayed his pass to suit Ashley Barnes's run but, when the3 pair did eventually combine, the striker fired wide.
The Reds had netted 48 times this term but were only able to register one shot on target against the Clarets in the first half.
Alex Oxlade-Chamberlain, one of seven changes made from the 2-1 win over Leicester City at Anfield, was the man responsible for that when collecting Adam Lallana's raking crossfield pass, travelling infield and forcing Nick Pope to save to his right.
Sean Dyche's side don't score many on home soil, just seven in 10 to be exact, but they tend to go on to win games when they do.
That moment almost arrived in the 18th minute when superb vision from Barnes and an even better execution looked to have set Johann Berg Gudmundsson free until Lallana made a vital interception.
Burnley came again when Emre Can's error put the visitors under pressure but Mignolet held on to Arfield's flick on at the near post after Steven Defour had clipped the ball in to the box.
After Mane dragged his shot wide when being afforded space to run in to, the home side went within a whisker of taking the lead.
And it was almost a carbon copy of the goal that had given them a surprise lead at Anfield back in September.
Again Arfield went for placement when the ball was cushioned in to his path on the edge of the penalty area by Barnes, stroking the ball towards the corner, but the attempt grazed the outside of the post with Mignolet stationary.
Liverpool took the lead on the hour and it was Mane that took a stand to prove that the club can cope without its three musketeers when necessary.
The Senegalese forward gave Pope no chance when bringing Alexander-Arnold's cross under control on the edge of the box before thumping the ball in to the roof of the net on the turn.
Defour tried to restore parity for the hosts almost immediately when allowing Arfield's pass to roll across on to his right boot but Mignolet was equal to the low drive.
The horrendous weather conditions would have been a goalkeeper's worst nightmare but Pope did phenomenally well to stay nimble to keep Alexander-Arnold's pile-driver out as the ball threatened deviate.
As play continued to switch Burnley went close again when Barnes adjusted his body position superbly to connect beautifully on the volley but his attempt sailed just wide of the upright.
When Pope showed a strong hand to prevent Oxlade-Chamberlain's thunderous strike from sneaking inside the near post and Mignolet kept substitute Sam Vokes's header out it seemed the one goal would decide this encounter.
However, there was still time for plenty of late drama. The Clarets equalised in the 88th minute and looked to have salvaged a point when Vokes flicked on Charlie Taylor's cross and Gudmundsson pounced, unmarked, at the far post to head home.
The Icelandic winger's first goal in over 13 months should have been enough but in the final minute of four added on in stoppage time the Reds added a other twist to the tail.
Burnley conceded late on at Old Trafford when failing to clear their lines from a Manchester United set-piece and the same happened once again.
Dejan Lovren's header from Oxlade-Chamberlain's free kick was heading in to the far corner but defensive partner Klavan helped it in on its way to make it 2-1.