The hosts had taken the lead in the second half courtesy of fine free kick from Steven Gerrard, who netted his 10th derby goal in his 32nd appearance.
However, the Toffees grabbed a late equaliser from an unlikely source as Phil Jagielka rocketed a sensational half-volley into the top corner via the underside of the bar.
Here, Sports Mole takes an in-depth look at another dramatic 90 minutes between these two great rivals.
On target: 8
On target: 5
Was the result fair?
A late goal always has the tendency to distort whether a side deserved a result or not, but Everton will consider themselves fairly fortunate to have come away with a share of the spoils in this match.
The first half was quite an even affair in general play, but it was Liverpool who threatened most and created the better chances throughout. Everton needed to rely on some good stops from Tim Howard to keep the scores level, while Simon Mignolet was not really worked in the Liverpool goal.
The hosts also spent much of the second half in control, limiting the Toffees' influence in the final third very well. However, as the match entered the closing stages, Liverpool began to sit back and invite pressure onto them, and that is always a dangerous ploy. No-one could have predicted quite how Everton would level the scores, but Liverpool certainly allowed Jagielka the space to venture so far forward.
It was a win over Everton at Anfield that kickstarted their campaign in the second half of last season, and they really could have done with a similar result this afternoon. There were plenty of improvements for the Reds compared to the matches against Aston Villa and West Ham United, but they are still far short of their best.
The hosts had 24 shots and created enough decent openings to put the game to bed long before Jagielka's stunning equaliser, so they only really have themselves to blame for not winning the match. Granted, a large chunk of their efforts were courtesy of Mario Balotelli from distance, but they also hit the crossbar from close range and worked Howard on a number of occasions.
To have not held on to the lead will be desperately disappointing for Brendan Rodgers, but his side's decision to sit back and attempt to soak up Everton's late pressure was perhaps a sign of a lack of confidence. Liverpool were at their best when bursting with confidence last season, and they will need to improve a lot more if they are to get that sort of swagger back.
Still not the free-flowing Everton were have become accustomed to seeing under Roberto Martinez, but like Liverpool there were definite improvements in this performance. Most notably, the Toffees were more solid defensively - although they did still allow the hosts a number of decent openings.
Going forward, the visitors failed to create too much, particularly in the second half as Romelu Lukaku struggled to impose himself upon the Liverpool defence. They required a late wonder strike from Jagielka to get anything from this match, and that is highly unlikely to happen again this season.
Everton are in a similar position to Liverpool in that they still need to improve a lot, but they do seem to be heading in the right direction. The biggest thing for Martinez going into this match would have been avoiding defeat, so he will be fairly content with the result and performance this afternoon.
Sports Mole's man of the match
Adam Lallana: There were no standout performances on either side this afternoon, but the player who looked most lively throughout - despite playing 120 minutes on Tuesday - was Adam Lallana. The midfielder was a constant thorn in the side of the Everton defence, closing down quickly and giving them no time at all. He also threatened when in possession himself with a few tricky runs into the area that brought risky challenges from the defenders.
This one goes to Balotelli for his miss shortly after Liverpool broke the deadlock. Just two minutes had passed since Gerrard's free kick flew into the top corner, and the striker had a glorious chance to double his side's advantage with a first Premier League goal for the club. However, from close range he could only cushion his volley onto the crossbar. Credit does have to go to Howard for a fine stop, but even so Balotelli really should have scored.
Merseyside derbies are never easy occasions for a referee, and Martin Atkinson started off very shakily this afternoon. He turned down an early Everton penalty shout for a tug on Lukaku by Alberto Moreno that could well have been given by either him or his linesman.
However, his biggest blunder came shortly afterwards when Raheem Sterling's strike hit the arm of Gareth Barry inside the box. It was a clear handball and penalty and, as Barry had already been booked, it would have had to have been a game-changing red card as well.
Liverpool: Next up for Liverpool is a trip to Switzerland to face Basel in the Champions League on Wednesday.
Everton: Everton are also in European action as they face an away trip to face Krasnodar in the Europa League.