Liverpool were lacklustre in the first half but produced a much improved second half performance to go to 2nd in the Premier League.
The reds travelled to Swansea keen to avenge the 3-1 defeat towards the end of last season. And with an upcoming international break the reds hoped to go into it with a solid position in the top four of the Premier League table.
There was one change to the Liverpool starting line up from the side that comfortably beat Hull City a week ago. Dejan Lovren returning to the Liverpool line up after recovering from illness - Ragnar Klavan moved back to the bench.
The Swansea boss pre-match was under some pressure with the Swans in 17th place but the mood lifted in the 8th minute when the home side took the lead. Almost inevitably it arrived from a corner. Sigurdsson sent the set-piece to the back post where the reds failed to defend it and it was headed back towards goal.
Dejan Lovren failed to focus on the ball which went past him and Leroy Fer got a toe-poke to put Swansea 1-0 up. Replays suggested it may have been marginally offside but it wasn't clear-cut.
The reds didn't launch an immediate fight back. Swansea had further chances to take the lead - Borja had already headed over on 5 minutes and they seemed to have the measure of Liverpool who looked tired and out of sorts.
Adam Lalllana appeared to pick up an injury after 20 minutes and eventually headed off down the tunnel. An enforced substitution at 1-0 down for Liverpool - Daniel Sturridge the man chosen to come on.
Towards the end of the half the reds did improve but they failed to get a shot on target in the half. Mane was the brightest of the Liverpool players - at one stage it required 4 Swansea defenders to dispossess him inside the box.
Daniel Sturridge was handed a yellow card after going down too easily in the penalty area. Klopp was animated on the touchline but will only have been massively frustrated at the first half display.
Liverpool came out stronger in the second half - possibly a half time rocket from the manager.
In the 55th minute the reds drew level. Coutinho's free kick hit the wall but Henderson looped in the ball back towards the penalty spot - Firmino connected with his head to send it past Fabianski.
Moments later Coutinho could have put the reds ahead - his powerful shot going narrowly wide of the goal.
A swagger returned to Liverpool's play as the sunshine came out in South Wales.
Swansea made changes - bringing on all three substitutes within the following 15 minutes and it settled the ship for them. They took the game back to Liverpool who looked uncomfortable when under pressure.
Karius flapped at a corner but the reds got away with it as the ball sailed over everybody.
With 6 minutes remaining the reds got the winner. Firmino was about to pull the trigger inside the box when he was fouled - up stepped James Milner who scored his third penalty in two games to make it 2-1 to Liverpool. Yet another comeback under Klopp completed.
Liverpool move up to 2nd in the Premier League and will end the weekend in a minimum of 4th position.