Darwin Nunez goal enough to maintain Liverpool's perfect ...

Darwin Nunez's first half goal earned them their 11th win in 12 games under Arne Slot but this was not their most convincing performance and they were living on their nerves towards the end as RB Leipzig pressed hard for the equaliser.

Two brilliant saves by Republic of Ireland international Kelleher inside a minute midway through the second half kept them in front while the Germans also had two goals disallowed for offside - one in each half.

Kelleher, playing because of the latest hamstring injury suffered by Alisson Becker, showed once again why he is good enough to be a No 1 keeper - whether it is at Anfield or elsewhere.

In fact, it was a tale of two goalkeepers because Leipzig's Peter Gulacsi - who spent five years at Anfield as a youngster without making a first team appearance - also made some fine saves to keep the Bundesliga team in the game.

As they did against Chelsea at the weekend, Liverpool were far from perfect but they are developing the happy habit of getting the win over the line and have matched Aston villa by making it nine points out of nine to top the table in Europe's revamped top club competition.

Slot also chalked up another record - it's the first time in their history that Liverpool have won their first six away games in a season. And that will certainly put them in good heart for Sunday's trip to title rivals Arsenal.

Leipzig are unbeaten in the Bundesliga but narrow defeats to Atletico Madrid and Juventus in their first two Champions League fixtures, meant they needed something from this game and looked the more dangerous team in the early stages.

Kelleher saved well from Amadou Haidara while Benjamin Sesko should have done better with a header chance he directed straight at the Liverpool 'keeper.

The normally unflappable Irishman then got lucky when he came out of his area but made a mess of a headed clearance and was left hugely relieved when Sesko couldn't find the open net with his curling shot.

Liverpool were fortunate again when Lois Openda's explosive shot into the top corner was ruled out for offside in the build-up but moments later Slot's team took the lead.

Salah's header from Kostas Tsimikas's cross looked like it would creep in at the far post but Nunez made sure by tapping it over the line.

That sparked Liverpool into belated attacking life and only a series of fine saves from Peter Galacsi - who spent five years at Anfield as a youngster - prevented them from being home and hosed by half-time.

He tipped over headers from Nunez and Virgil Van Dijk and was relieved to see Cody Gakpo's shot find the side netting.

Nunez should have had a clear penalty when he was upended by Henrichs - with VAR inexplicably not asking the referee to review his decision.

Galacsi was Leipzig's hero again early in the second half when he saved from Gakpo's close range effort after a comedy of errors by the German club's defence.

Salah didn't look too pleased when he was replaced by Luis Diaz in the 63rd minute especially as Liverpool needed a second goal to feel safe.

Alexis Mac Allister nearly got it when his shot clipped the bar after being set up by Dominik Szoboszlai.

But the game remained in the balance and Liverpool needed two brilliant saves inside a minute to remain in front.

First, Sesko looked certain to score only to be denied by Kelleher's outstretched leg. Then moments later Kelleher made an acrobatic tip over save to keep out Simons' dipping shot.

Liverpool's luck continued when Openda was clean through but instead of shooting he tried to square the ball to Poulsen and the pass went behind his team-mate as slot's men followed up their earlier group wins over AC Milan and Bologna to virtually make sure of their passage to the last 16 with five games left to play.

But they will want to finish in the top eight rather than the top 16 of the table to ensue they go straight into the knock-out stages without having to deal with a play-off tie.

RB Leipzig ( 4-3-3): Gulacsi 8; Henrichs 6, Geertruida 6, Orban 6, Lukeba 6; Vermeeren 6, Haidara 6, Openda 6, Simons 6 (Poulsen 77, 5), Nusa 6, Sesko 5.

Liverpool (4-3-3); Kellerher 9; Alexander-Arnold 6 (Gomez 74, 5), Konate 7, Van Dijk 7, Tsimikas 7 (Robertson 75, 6); Szoboszlai 7, Gravenberch 6, Mac Allister 6; Salah 6 (Diaz 63, 6), Nunez 7 (Jones 75, 6), Gakpo 7.

Referee: Sandro Scharer (Switzerland).