James Milner netted a late penalty as Liverpool came from behind to beat Swansea City 2-1 and pose further questions over Francesco Guidolin's future at the Liberty Stadium.
Leroy Fer's fourth Premier League goal of the season put the Swans, whose last home win came against Liverpool in May, ahead in the eighth minute.
Liverpool lost Adam Lallana to a groin injury during a first half in which they failed to register a shot on target, a far cry from the 5-1 win over Hull City last time out.
But Jurgen Klopp's side quickly addressed that in the second half, as Roberto Firmino headed them level.
And Guidolin, who has not tasted victory in the league since the opening-day win over Burnley, was left empty-handed again when shambolic defending led to Angel Rangel fouling Firmino in the box, Milner scoring his fourth spot-kick of the campaign.
Mike van der Hoorn had the chance to equalise deep in stoppage time but volleyed horribly wide from five yards out.
Both sides made one change from their previous outings, Borja Baston earning a first Premier League start for the hosts in place of the injured Fernando Llorente, while Klopp brought in Dejan Lovren for Ragnar Klavan.
Swansea adopted the same positive approach that won them plaudits, but no points, against Manchester City last weekend and Borja missed an excellent opportunity to put them ahead early on, heading well over the crossbar from Wayne Routledge's teasing cross.
But the home side shrugged off that miss, taking the lead two minutes later when Borja's back-post header was touched on by Van der Hoorn and prodded home by Fer.
The Dutchman then blazed over the target with an ambitious 13th-minute effort as Guidolin's men continued to press.
Liverpool suffered a further setback when Lallana hobbled off, Klopp eventually introducing Daniel Sturridge, but only after Jack Cork had almost toe-poked past Loris Karius when the visitors were down to 10 men.
Gylfi Sigurdsson's set-piece delivery again exposed the Reds, but Borja's off-target header came as the linesman's flag went up for offside.
Liverpool left if late in the half to present any serious attacking threat, with Jordi Amat making timely interventions to block Nathaniel Clyne's low cross and Sadio Mane's shot on goal, while Sturridge was booked for a dive following minimal contact in the box from Routledge.
Firmino finally had Liverpool's first shot on target in the opening two minutes of the second half and Amat was again on hand to clear the danger when Mane looked to find a way past Lukasz Fabianski.
The Pole was beaten, however, when Jordan Henderson lifted a searching ball in for Firmino to flick a header into the goalkeeper's bottom-right corner after 54 minutes.
That set the stage for a spell of Liverpool dominance, with Philippe Coutinho curling narrowly wide from 20 yards following excellent build-up play.
Assiduous work from Milner to dispossess Van der Hoorn created a glorious opening 20 minutes from time, but his pass was slightly behind Mane and the Senegalese's strike was diverted over by Kyle Naughton.
But the pressure finally told six minutes from time as Modou Barrow skied a clearance inside his own box, with Rangel compounding the error by piling into Firmino.
Milner sent Fabianski the wrong way as Liverpool made it five wins in a row in all competitions, while Guidolin's men - who saw Van der Hoorn scuff wide from close range at the death - are six without victory in the league.