Diogo Jota's second-half header secured a 2-1 win for Liverpool over struggling Sheffield United at Anfield on Saturday but the Premier League champions were made to dig deep for the points.
Liverpool were seeking a first win in three league games and in a frantic start to the encounter they fell behind in the 13th minute when Sander Berge netted from the penalty spot.
Sheffield United, looking for their first win of the season, could have doubled their lead but Roberto Firmino levelled in the 41st minute with a tap-in.
Jota then rose to thump home a header in the 64th minute, shortly after Mohamed Salah had a goal ruled out by VAR.
Unconvincing it was but Liverpool extended their unbeaten run at Anfield to 62 games in the Premier League and moved joint top with Everton on 13 points, although their Merseyside rivals play against Southampton on Sunday.
Sheffield United more than matched Liverpool in spells throughout the game but remain second from bottom with one point from their opening six games.
"I am only interested in the mentality in our changing room and I see hunger, resilience, character to dig in and win if you are not playing at your best," Liverpool skipper Jordan Henderson said. "We showed we can dig in and see results out."
United keeper Aaron Ramsdale was in the thick of the early action, almost gifting Liverpool a goal after getting caught in no man's land but Sadio Mane's shot was hacked clear by John Egan. Ramsdale then had to back-pedal to tip over an audacious free kick from near the halfway line by Trent Alexander-Arnold.
It was the visitors who took the lead, however, when Fabinho made contact with Oli McBurnie right on the edge of the penalty area and the referee Mike Dean awarded a free kick.
Yet VAR checked the decision and ruled that the tackle had taken place inside the area, although it looked inconclusive.
Berge calmly sent Alisson the wrong way.
Sheffield United left back Ben Osborn went close to a second when he met a cross with a powerful volley but Alisson saved it.
Liverpool were struggling to assume control but got level shortly before the break when Mane's close-range header drew a reaction save from Ramsdale but the ball fell kindly for Firmino to sidefoot into an empty net.
Things did not get any easier for a labouring Liverpool after the break and the visitors had a decent chance when Berge headed a ball down for George Baldock who fired wide.
Salah thought he had put Liverpool ahead just past the hour with a brilliant dinked finish after a deft control but VAR ruled the Egyptian marginally offside.
But any sense of injustice was quickly wiped away as Jota timed his leap to perfection to head past Ramsdale.
Still Sheffield United threatened and substitute David McGoldrick rifled a half-volley just over with his first touch.
At the other end Salah was denied by the woodwork after another exquisite piece of skill and Liverpool were relieved when the final whistle arrived.