It was the late late show at Turf Moor as the reds beat Burnley thanks to a 94th minute goal from Ragnar Klavan, with the assist from Dejan Lovren.
The reds thought they had already done the hard work when Sadio Mane scored on the hour, but a late equaliser from Gudmundsson had the Burnley crowd thinking they had stopped the reds in their tracks.
But in the final minute of the game, Lovren rose highest from a free kick and sent it goalbound with Klavan notching the ball over the line.
Klopp makes changes
The reds had made 7 changes following the game 48 hours ago with Adam Lallana making his first start of this season.
Simon Mignolet also returned to the side and with Milner moved to the bench, he captained the reds team in his 201st appearance.
The game was played in tough weather conditions - plenty of rain and swirling wind to see in the New Year at Turf Moor. Sean Dyche's side made just one change with Tarkowski returning after suspension.
Liverpool didn't look anywhere near as fluid as they had in recent weeks and despite solid first half possession it was Burnley who had the pick of the chances.
The reds looked like they had more purpose in the second half and on the hour, with Klopp beginning to think about substitutions, Sadio Mane collected the ball at the edge of the area from a deflected cross and turned and smashed the ball in with his left foot.
Late goals for both sides
But Burnley are a decent Premier League side these days and eventually their perseverance paid off when a ball deep in to Liverpool's area was poorly defended and Mignolet could only watch as Gudmundsson headed in at the back post.
The sting in the tail was still to arrive.
With one minute of normal time remaining a Liverpool free kick was sent in to the area. Lovren angled his header towards the goal taking out keeper Nick Pope and Klavan rushed in to get the ball over the line.
It's a big three points for Liverpool who move on to 44 points, and temporarily level with Man Utd in 3rd place.