The visitors took an early lead in the game, with Wissam Ben Yedder capitalising on some poor defending to tap home from close range.
However, the Reds came roaring back, equalising through Firmino before Mohamed Salah added a second, thanks to a big deflection off Simon Kjaer.
Firmino then missed the opportunity to further extend their lead, firing his spot kick against the post, before Correa equalised on 72 minutes.
There was further misery for the Reds late on, with Joe Gomez picking up a second yellow card in stoppage time, as Jurgen Klopp's side finished the game with 10 men.
Liverpool made three changes for the game with Loris Karius, Gomez and Dejan Lovren all coming in. Here's a look at the team sheet, via Melissa Reddy of Goal:
Melissa Reddy @MelissaReddy_
Full #LFC v #SevillaFC teamsheet from Anfield https://t.co/b6zOe80f9g2017-9-13 17:54:05
Yet the hosts got off to the worst possible start with Sevilla taking the lead after just five minutes at Anfield.
Correa whipped in a low cross from the left, which should have been cleared by Lovren at the near post but went through to Ben Yedder to tap home from close range.
ITV sports presenter Jacqui Oatley made it clear who she felt was to blame for the opener:
Jacqui Oatley @JacquiOatley
Inexplicably horrendous defending by Lovren and co for #LFC….2017-9-13 18:53:34
The goal produced an instant response from Liverpool, with Sadio Mane denied a free-kick on the edge of the box after a clash with Nicolas Pareja, before forcing goalkeeper Sergio Rico into a good save with a low shot.
The Reds continued to press and were finally rewarded after 21 minutes, when Alberto Moreno played a quick one-two with Jordan Henderson before crossing for Firmino to fire home from close range.
ESPN FC's Mark Ogden was not impressed with the visitors' defending for the goal:
Mark Ogden @MarkOgden_
1-1 Firmino. More bad defending, this time by Sevilla, for another tap-in2017-9-13 19:06:35
Liverpool might have added a second within minutes, but Can pulled his low shot wide after being found by Mane.
However, the second goal did not take too long to come. Salah won the ball back on the edge of the box in a challenge with Steven N'Zonzi, before firing a low shot that deflected off Kjaer's boot past Rico in the 37th minute.
There were protests from the visitors about the goal, as they believed Salah had fouled N'Zonzi, but it was a deserved lead for Liverpool, according to Reddy:
Melissa Reddy @MelissaReddy_
Mohamed Salah's determination to get back, win possession and get a shot off deserved a second for #LFC. Deflection off Simon Kjaer. 2-12017-9-13 19:23:27
The evening could have got even better for Liverpool as the Reds were awarded a penalty just before half-time after Pareja tugged down Mane in the box, moments after appearing to handle the ball, which went unnoticed by the referee.
Firmino stepped up, but he was denied by the woodwork, with his shot beating the goalkeeper but striking the post and flying away to safety.
Sevilla suffered more misery in the second half, with coach Eduardo Berizzo sent off after twice throwing the ball away after it had gone out of touch for a throw.
The home fans were delighted at the departure of the visiting coach, as noted by Henry Winter of The Times:
The chances continued to fall for Liverpool, with Georginio Wijnaldum smashing a low shot that Rico just about managed to parry. But they were made to pay for not extending their lead further in the 72nd minute.
Luis Muriel picked up possession from a throw, before finding Correa free in the box and he made no mistake, flicking the ball past Karius to make it 2-2.
Klopp responded by sending on Philippe Coutinho for Can, with the Brazilian welcomed back by the home crowd, after a summer of transfer speculation, as noted by ESPN FC's Glenn Price:
Glenn Price @GlennPrice94
Coutinho on for #LFC. He gets a good reception from the crowd. 15 minutes left to find a winner. https://t.co/QjVv7wFVGw2017-9-13 20:19:52
However, the best chance of the closing stages fell to Sevilla. Muriel got free and fired inches wide in stoppage time before Gomez picked up a second yellow card as Liverpool ended the game with 10 men.
It will feel like a disappointing result for Liverpool, after leading for a long spell and passing up a golden opportunity to make it 3-1.
However, the two teams still look the strongest in the section and will remain confident of progressing to the knockout stage, with NK Maribor having held Spartak Moscow 1-1 in the other game in Group E.