Liverpool's Anfield fortress was briefly shaken by Tottenham Hotspur but Juergen Klopp's side recovered to secure a 2-1 win and restore their six-point lead atop the Premier League on Sunday.
Manchester United claimed their first away league victory of the season, beating Norwich City 3-1 despite missing two VAR-awarded penalties, and Arsenal squandered a two-goal lead to draw 2-2 at home to Crystal Palace.
Newcastle United remained one point above the bottom three after drawing 1-1 at home with Wolverhampton Wanderers.
Liverpool's unbeaten Premier League run at Anfield now stands at 45 but when Harry Kane put Tottenham in front after 48 seconds and the visitors led at the interval it appeared their marauding start to the season was in danger of ending.
Kane headed in after Son Heung-min's deflected shot struck the woodwork and the visitors led a charmed life as their keeper Paulo Gazzaniga pulled off some superb saves.
Son also hit the bar early in the second half but Liverpool equalised soon after through Jordan Henderson before Serge Aurier's rash challenge handed Liverpool a penalty which Mohamed Salah tucked away.
Liverpool survived late scares but moved to 28 points from their opening 10 games — two more than they earned from the same period last season when they went on to finish runners-up to Manchester City. City, who beat Aston Villa on Saturday, have 22 points.
Tottenham, in 11th place after a fourth defeat of the season, find themselves in the bottom half of the table heading into November for the first time under Mauricio Pochettino.
The only bright note was Kane's opportunist effort which took him to equal third with Martin Chivers on Tottenham's all-time scoring list on 174 goals.
VAR reared its head again elsewhere on Sunday.
Manchester United were awarded two penalties in the opening half against Norwich, the first after referee Stuart Attwell appeared rightly to not give a spot-kick when United's Daniel James and Ben Godfrey tangled.
United were awarded another penalty via VAR for a Todd Cantwell handball. Both were saved by Tim Krul, the first from Marcus Rashford and the second from Anthony Martial.
First-half goals by Scott McTominay and Rashford and one from Martial after the break ensured the misses did not matter too much.
"VAR is there to help but when it takes ages like the first penalty, it is not a clear and obvious error," United manager Ole Gunnar Solskjaer, whose side climbed to to seventh, said. "When it took that long, it is a signal that it should not have been."
Arsenal were 2-0 up at home to Palace inside nine minutes with goals from Sokratis Papastathopoulos and David Luiz.
Palace halved the deficit when Luka Milivojevic scored from the spot following a VAR intervention after referee Martin Atkinson had initially booked Wilfried Zaha for diving.
Jordan Ayew headed Palace level in the 52nd minute but VAR was again in action when Sokratis thought he had won it for the hosts in the dying minutes but his effort was ruled out for a foul by Callum Chambers on Gary Cahill.
It left Arsenal four points behind fourth-placed Chelsea who won at Burnley on Saturday. Palace are sixth.
"For me there is no confusion — it is not a good decision," Arsenal manager Unai Emery said.
"We deserved to win, we had a good reaction after they equalised, we scored but then they didn't count it."
Jonny rescued a point for Wolves after Jamaal Lascelles had given Newcastle the lead. The hosts ended with 10 men after Sean Longstaff was sent off.