Swansea City took the lead through Leroy Fer’s fourth goal of the season, the midfielder met Borja Baston’s header from the back post and prodded home from a few inches away.
Liverpool equalised ten minutes into the second half, as a wide-open Roberto Firmino headed past Lukasz Fabianski.
James Milner sealed the win from the spot, after Angel Rangel brought down Firmino. The full-back now has four goals for the season.
Swans take charge earl on
Swansea were the better side in the first half, as Baston headed two efforts off target either side of Fer’s goal.
The first chance was just five minutes into the game, latching onto a good cross from Wayne Routledge but Swansea’s record signing mistimed his jump and headed well over.
His second chance came twenty minutes later, in an offside position from Gylfi Sigurdsson’s free kick as the striker headed just wide.
Fer’s goal came from a Sigurdsson corner, lofted into the back post towards Baston. His knock-down was flicked on by Dejan Lovren until the Dutch midfielder turned a shot in.
Swansea pressed Liverpool very well, Jack Cork in particular made a nuisance of himself as the away side’s defence struggled to pass out from the back.
Sigurdsson was in mid-season form, chipping a ball over to Cork as he tried a shot but he couldn’t get a good connection and Karius saved easily.
Liverpool ended the half well, but didn’t create any clear-cut opportunities.
Liverpool bounce back to take all three points
The Reds’ best chance fell to Sadio Mane, who went through on goal from a through ball but his shot was well blocked by Jordi Amat.
Liverpool started the second half brightly, testing Fabianski twice early on but the Polish goalkeeper was equal to Firmino and Mane’s efforts.
The away side equalised from a set-piece, Coutinho’s free kick hit the wall but the resulting delivery from Henderson found Firmino free in the area, and he headed home.
Liverpool kept piling on the pressure, as Philippe Coutinho curled an effort just wide following Georginio Wijnaldum’s lay off from 20 yards.
Mane had another good chance, as Mike Van der Hoorn lost possession inside his own box, the ball falls to Mane and his shot was blocked by Kyle Naughton.
Liverpool were awarded a penalty with ten minutes left as Angel Rangel clumsily fouled Firmino following a sliced Modou Barrow clearance. Milner finished with ease.
Van der Hoorn had a golden chance in stoppage time, a cross found him in acres of space from six yards out but the defender couldn’t hit the target.
Swansea’s first-half performance should ease some of the concerns regarding Francesco Guidolin’s job, but football is a results business and the Welsh side still haven’t won since the opening day of the season.
The result takes Liverpool second in the table, Swansea remain 17th but could drop into the relegation places should teams below them pick up points.