Mohamed Salah scored his 100th Premier League goal for Liverpool but it was not enough to beat Brentford, who twice pegged the Reds back in a breathless 3-3 draw.
Jurgen Klopp's side were unable to reap the maximum profit from slip-ups by Manchester United and Chelsea earlier in the day as they shared the points after an early-evening cracker in west London.
Instead they moved just one point clear at the top, while preserving the top flight's only remaining unbeaten record.
And Klopp will be relieved at that after Ivan Toney had what would have been a late winner ruled out for offside.
The German will also know his side will not face many tougher trips all season, with vibrant Brentford leading through Ethan Pinnock and, following goals from Diogo Jota and Salah, equalising through Vitaly Janelt.
Then, when Curtis Jones smashed Liverpool ahead again, Bees sub Yoane Wissa came up with another equaliser.
There was a taste of things to come when both teams were denied by goal-line clearances in the opening 10 minutes.
First Salah missed out on a seventh-minute opener thanks to a spectacular piece of defending from Kristoffer Ajer.
Jota's through-ball sent Salah through and he rolled his shot past Bees goalkeeper David Raya, but Ajer raced back and slid in to hook the ball off the line.
Moments later, at the other end, Bryan Mbeumo latched onto Toney's flick-on and lifted the ball over Alisson, but this time Joel Matip got back to scoop the ball clear from underneath the crossbar.
Brentford were more than holding their own against the 2020 champions and were good value for the lead they took in the 27th minute.
Spanish winger Sergi Canos, who spent three years at Liverpool as a youngster but played only nine minutes for the first team, got down the Reds' right and drilled in a low cross.
Toney helped the ball on at the near post and centre-half Pinnock was left with a tap-in.
The lead lasted barely three minutes, however, before Jordan Henderson swung in a cross from the right and Jota headed home at the far post.
Seven minutes before the interval Henderson teed up Jones on the edge of the area and his shot was deflected onto a post by Pinnock.
Jota should have been celebrating his second of the afternoon from the rebound but somehow Raya got his body in the way of the shot and it flew wide.
After the break Salah grabbed his landmark goal. The Egypt striker was initially flagged offside as he tucked away Fabinho's ball over the top, but a VAR check showed he was in fact onside.
Back came Brentford, though, and when Pontus Jansson slid in to crash Ajer's cross onto the bar, Janelt popped up at the far post to force the loose ball home.
Jones blasted Liverpool back in front in the 67th minute. Moments after sending a long-range sighter high into the stands, the midfielder took aim again and his low drive took a deflection in a crowded penalty area as it flew past Raya.
Salah should have had goal number 101 after he was played in by Sadio Mane but he chipped the ball onto the roof of the net.
Moments later Bees sub Wissa arrived at the far post and produced a composed finish to equalise yet again, before Toney was denied a late winner by the linesman's flag.