Liverpool could only take a point from an astonishing game as Arne Slot and Anfield raged at referee Tony Harrington.
Substitute Diogo Jota came off the bench to grab the Reds' second equaliser in a game which saw Andy Robertson sent off in the 17th minute.
The tone for the game was sent inside the first few seconds when Issa Diop lunged into a challenge on Robertson that he was lucky to escape with just a yellow card for after a VAR check.
Referee Harrington would find himself in the thick of the action as he brandished four yellow cards and a red in the first half hour, but Fulham carried a threat amid the madness and took the lead nine minutes in.
Harry Wilson started the move with a fine ball to Alex Iwobi, and after the former Evertonian had played Antonee Robinson in down the left, the impressive full-back's cross looked as though it had been overhit, but Pereira had other ideas.
The Brazilian impressively adjusted his body to strike a volley that flicked off Robertson and beat Alisson at his near post to stun the Kop.
Having had pain inflicted upon him for the second time in the space of 10 minutes, if Robertson thought that was as bad as his day was going to get then he had a shock coming.
Robertson allowed a Sasa Lukic pass to slip away from him, and the lively Wilson was quicker to the ball than his direct opponent.
As the Scot scrambled he brought down the wily Welshman, and after further VAR checks for both offside and whether or not Virgil van Dijk was on the cover, Harrington's red card stood.
Anfield reacted in a stunned silence, but after Slot shuffled his pack with Ryan Gravenberch often dropping back into defence, the depleted Reds set about their task.
Diaz should have done better with a header over the bar, but Fulham were dealing with Liverpool's threat impressively, with Robinson and centre-back Jorge Cuenca - on his first Premier League start - standing out.
Slot opted against making changes at the break, perhaps relying on the emotion of Anfield to drive his 10 men on, and it just that two minutes into the second half when Mo Salah’s cross was headed in at the back post by a diving Cody Gakpo to spark a roar of defiance.
Liverpool had their tails up now and wanted a penalty when Kenny Tete caught Joe Gomez, Fulham always carried a threat though and Wilson should have done better from an Iwobi pass. Slot raged on the sidelines and would eventually pick up a yellow card.
As the game entered the final half hour the relentlessness continued, and Salah fired wide after being found by Dominik Szoboszlai after a lightning break.
Fulham continued to pose a threat going the other way though, and after the introduction of Muniz it was through the superb Robinson that they struck again.
The full-back escaped down the left, and when he pulled the ball back it was Muniz who arrived like a train to tuck home.
Slot did now turn to his bench in search of answers, and in Jota he found one.
The Portuguese, back for his first appearance since October, took a Nunez pass and fired in at the Kop end to make it 2-2.
Jota then almost won it after an almighty scramble in stoppage time only for his effort to deflect wide.
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