Liverpool made it seven wins from seven, as an error from goalkeeper Dean Henderson gifted them all three points at Sheffield United.
Liverpool had failed to generate a shot on target for the first 69 minutes, but bang on the 70 minute mark Georginio Wijnaldum fired low and slow from the edge of the area right at Henderson.
The keeper had been a spectator for most of the match and that possibly led to a lack of concentration, as he let the ball tamely through his legs and it crept over the line.
It was harsh on the Blades who had created the better chances, without fully testing Adrian in the Liverpool goal, and Liverpool know they got away with one at Bramall Lane, highlighted by the Liverpool stopper being booked for time wasting on just the 83rd minute.
It is now 16 straight league wins for Liverpool, and 24 unbeaten in total, while the South Yorkshire club are still looking for their second home league victory of the campaign.
United's well-drilled 5-3-2 formation gave the visitors more problems than they would care to admit considering the attacking talent they had at their disposal with their build-up play laboured and lethargic.
And with Oli McBurnie a danger on the counter-attack down the left there was even the threat of even more trouble with the striker testing Adrian early on.
United were so concentrated on maintaining an organised front in the face of their opponent's domination of possession they were almost surprised when chances came their way with Callum Robinson snatching a shot wide after being put through by John Fleck.
Liverpool toiled in the middle third, moving the ball one way and then recycling it back the other as they probed to make a breakthrough with half-chances missed by Wijnaldum, Mohamed Salah and Andy Robertson.
The direct approach proved more profitable as Virgil Van Dijk lofted a pass for Mane to run clear of the defence but he sliced high and wide with only goalkeeper Henderson to beat.
Mane should have done better with that effort but the one two minutes before the break was even more inexplicable.
Wijnaldum launched Salah on the counter-attack which resulted in Firmino, seven yards out, opting to tee up Mane but although his shot beat Henderson at his near post the upright denied him a goal.
Liverpool's seven first-half shots were the most they had produced in the opening 45 minutes of a league match without one being on target since February 2017, when they lost to Hull.
After more labouring without intent in the opening 20 minutes of the second half Klopp changed tack, sending on the fit-again Divock Origi for Jordan Henderson and switching to a 4-2-3-1 formation with Salah as its spearhead.
The best chances were still falling to the hosts, however, with Norwood forcing to tip a low drive around the same post Mane had struck until Liverpool benefited from a huge stroke of luck.
Just when it seemed United were about to become only the only side after Barcelona and Napoli in the last 26 games to prevent the Reds scoring, Henderson blew it.
Wijnaldum's shot from the edge of the area was hit well but more in hope than expectation but, as it flew through a crowd of players, United's goalkeeper failed to get a proper hold and it slipped between his hands and then his legs to trickle over the line.
Henderson's sticking out a leg to deny Salah clean through one-on-one prevented it becoming 2-0 but the damage had been done.
Nevertheless, substitute Leon Clarke should still have equalised five minutes from time but ballooned over Fleck's low cross from close range.
Liverpool's bandwagon rolls on, briefly extending their lead over Manchester City to eight, having taken an incredible 121 points from a last possible 138.