Dominic Calvert-Lewin's header salvaged a 2-2 draw for Everton in a controversial 237th Merseyside derby at Goodison Park that saw Jordan Henderson denied a late winner by VAR.
Everton goalkeeper Jordan Pickford had been lucky to escape conceding a penalty and being sent-off early in the first half for a knee-high challenge on Virgil van Dijk, which ended the Dutch captain's afternoon.
Henderson thought he had won it in the five minutes of added time against 10 men when Pickford fumbled his shot but the goal was ruled out for the tightest of offside decisions against Sadio Mane.
It was another contentious decision which meant the defending Premier League champions made the short trip home aggrieved at what they perceived a failure of VAR.
Manger Jurgen Klopp, who admitted after the match that van Dijk's injury "doesn't look good", said: "The performance was top, it was a top game and a good game for both teams.
"We were dominant against a side full of confidence and with a clear plan. It was probably the best away game since I was at Liverpool. I saw a really good performance.
"I would be more happy if we win but I wanted to see a response and see the team we were before."
On the Henderson ruled-out goal, he added: "I don't know where the line is where you can do offside.
"Yes, we should have won this game. The boys played a super game. against a side with quality and confidence. Dominating from the first second is absolutely exceptional."
The champions had been humiliated 7-2 by Aston Villa just before the international break but they quickly set about putting things right when Mane scored in the third minute, firing home a low cross from Andy Robertson.
Everton took advantage of Van Dijk's absence when Michael Keane rose at the near post to power a header from a corner past Adrian after 19 minutes.
Liverpool were on top for long stretches and Mohamed Salah restored their lead in the 72nd minute, pouncing on a headed clearance from Yerry Mina and drilling a drive past Pickford.
But Everton, determined not to lose their unbeaten record, got back on level terms when James Rodriguez sent Lucas Digne down the left and his perfectly floated cross was headed home by the leaping Calvert-Lewin.
Everton's Brazilian forward Richarlison was sent off in the 90th minute after a wild challenge on Thiago Alcantara.
Calvert-Lewin said: "As you'd expect in derbies got tackles flying in 50-50, so there's always a chance the ref might bring out a yellow or red.
"Disappointed we didn't kick on at 1-1. We knew had spells where we wouldn't have the ball. I managed to put one away but I genuinely thought it would be coming [the win], but it wasn't to be.
"I can't put my finger on why we came out slow, momentum was on our side but sometimes it happens. But we've made strides and got ourselves back in to the game and we had the chances to win it but we didn't take them today.
"I'm disappointed we didn't win the game. We wanted to win the game. In that respect it was frustrating. In terms of the bigger picture it's a point and we'll take it."
Manager Carlo Ancelotti said his team's performance has given him "confidence" for the rest of the season.
"It was terrific. It was a good game in general. Exciting game. Lot of fight, lot of pressing, lot of intensity.
"We competed with them. We were 1-0 down and equalised, 2-1 down and equalised. It was a good test and I have a good feeling.
"To know we can compete with the champions of the last season it gives us more confidence for the future."
Despite dropping points for the first time this season, goalscorer Keane said the club should be pleased with the progress made since last season.
"We've definitely improved," he said. "The new lads coming in have been brilliant. The mentality has changed. We conceded early today and years gone by we might have conceded another, but today we came back.
"Derbies are special days. It still has a special feeling. Gutted the fans weren't here."