James Milner's late penalty gave Liverpool a hard-fought victory over Swansea, increasing the scrutiny on Swans boss Francesco Guidolin.
Leroy Fer gave the hosts a first-half lead when he steered the ball home from close range at the back post after Baston Borja's knockdown from a corner.
Roberto Firmino levelled shortly after half-time when he headed in from Jordan Henderson's cross.
Milner netted the winner six minutes from time after Firmino was fouled.
The Liverpool midfielder's goal was just reward a dominant second half from his team, who have now won four Premier League games in a row.
It was, however, a little cruel on Swansea, whose spirited performance has probably bought Guidolin a little more time to turn things around.
The Swans remain one point above the relegation zone and have not won in the league since the opening day of the season.
But the club's owners had indicated before the game that the manner of performances would have as much of a bearing on Guidolin's future as the results.
Reds show powers of recovery
Liverpool arrived in south Wales on a high, winning their past three league games and scoring 11 goals in the process.
Despite his side's fluency in attack, manager Jurgen Klopp had expressed concerns about the Reds' fragility from set-pieces, and his fears proved well founded as they fell behind in scrappy circumstances.
Rattled by their opponents' energetic pressing, Liverpool conceded a corner and, from it, Swansea's £15m record signing Borja headed across goal for Fer to turn the ball in from a yard out.
The ragged visitors could have conceded another had Borja not been so wayward with a free header - and Liverpool fans may have feared another hard lucky story, akin to their only defeat of the season at Burnley, on 20 August.
However, the visitors were vastly improved in the second half as they recaptured their recent impressive form and equalised thanks to more unsteady set-piece defending, as Firmino headed in from close range.
Klopp's side dominated from that point and, after they were initially thwarted by dogged Swansea defending, they eventually struck when Angel Rangel pushed Firmino in the back and Milner calmly converted the penalty.
Guidolin's uncertain future
In stark contrast to their high-flying opponents, Swansea entered the game in the midst of a torrid spell chairman Huw Jenkins described in the match programme as the hardest of his 12 years at the helm.
Guidolin's future remains in the balance, with his side just one point above the relegation zone and without a league win since beating Burnley on 13 August.
His players responded to his plight superbly, harassing Liverpool with a high-octane first-half display.
However, they were overwhelmed after the interval and were powerless to stop Guidolin suffering a third successive league defeat for the first time in his tenure.
His position is now as uncertain as ever.
Although Swansea's owners have started compiling a shortlist of potential successors in the event of Guidolin's sacking, they indicated beforehand that the Italian would be given time to turn the club's fortunes around.
Swansea boss Francesco Guidolin:
"The players gave me a good answer. Our relationship is good. There is no problem between me and my players.
"I don't know [about the future]. It's not my decision. It's just for me to prepare for the game and the team. I know the situation. It's a possibility. The important thing is to prepare with patience.
"Before the game I saw the new owners Jason [Levien] and Steve [Kaplan] just to say 'hello'. I don't know if in the next day there's meeting."
Liverpool manager Jurgen Klopp:
"I thought we could have done better in the first half. Our body language was not good, we were static and it was easy to defend against us. We are not as good as we should have been.
"You have to show why we are here. We showed a reaction, were more organised, clear in all situations and we deserved to win. Of course I am happy we have had two or three brilliant games in a row.
"If Milner is our top scorer at end of the season with penalties, I have no problem with it. All is good. The performance was not perfect but it was good enough."
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