Philippe Coutinho had Liverpool deservedly in front at half-time, the Brazil international beating Petr Cech with a deft header after Mohamed Salah's cross looped up off Laurent Koscielny.
But while Jurgen Klopp's side dominated the first period, they were later left to rue missed chances.
An epic second half initially saw a rampant Liverpool double their advantage shortly after the restart, Salah's shot deflecting in after Firmino led a superb counter-attack.
Their two-goal lead was short-lived, though, as a resurgent Arsenal were in front with three goals inside five remarkable minutes.
Alexis Sanchez headed through the legs of Simon Mignolet from Hector Bellerin's pinpoint right-wing cross, and then the goalkeeper was beaten too easily by Granit Xhaka's viciously swerving drive.
The comeback was seemingly complete thanks to Mesut Ozil's sensational finish, the playmaker chipping Mignolet after a sublime one-two with Alexandre Lacazette, but Firmino beat Cech with 19 minutes left to level the match.
A draw was certainly the fairest outcome in a thrilling contest, with Firmino's intervention ensuring Arsene Wenger is yet to beat Klopp's Liverpool in five attempts.
After throwing away another lead, Liverpool stay fourth - a point and a place above Arsenal - but the dreadful defending from both sides indicated they will struggle for Champions League qualification without improvement at the back.
388 - There were just 388 seconds between Liverpool going 2-0 ahead and Arsenal taking the lead to make it 3-2. Rapid. #ARSLIV— OptaJoe (@OptaJoe) December 22, 2017
Despite Jordan Henderson limping off early and Arsenal's pressing high up the pitch, the visitors had the better of the opening exchanges and Coutinho bent a curling effort narrowly wide.
Firmino should have done better with a pair of back-post headers from deep left-wing crosses but Liverpool opened the scoring after 26 minutes.
Milner sent Salah one on one with Koscielny in the right channel and, while the France defender did well to hold up the in-form forward, Coutinho flicked in his first ever Premier League headed goal after the cross took a kind deflection.
Firmino's drive narrowly cleared the crossbar just after the half-hour mark and Cech then had to deny Salah after Koscielny's slip let the Egypt international in, with Sadio Mane acrobatically turning the rebound over.
Arsenal left the field to boos from the Emirates crowd after a mistake-ridden first half saw the hosts fail to muster a single shot on target, with Liverpool eyeing a repeat of August's 4-0 rout.
Wenger replaced the injured Nacho Monreal with Shkodran Mustafi at the interval, but Liverpool's dominance continued, Salah adding a second after the Reds countered at speed.
Liverpool won the ball deep in Arsenal territory and, with the Gunners short at the back, Firmino fed the Premier League's top goalscorer Salah for his 15th top-flight strike of the season, his strike taking a slight deflection.
Arsenal responded immediately in an incredible spell, Sanchez starting the comeback by nodding in Bellerin's centre to ensure his side have now scored in 24 consecutive home league matches.
Xhaka let fly from 25 yards, with late movement from the strike beating Mignolet, although the goalkeeper really ought to have done better, before a delightful goal put Arsenal in front.
Ozil fed Lacazette, who neatly played a backheel into his team-mate's path, and the Germany international's cute chip left Mignolet sprawling.
Goals continued to flow, though, with Liverpool levelling through Firmino when Cech was unable to keep out the forward's effort despite getting a strong hand to the shot.
Sanchez almost beat Mignolet at his near post before the late introduction of Alex Oxlade-Chamberlain off the bench created the enticing possibility of the former Gunners midfielder punishing his former employers.
Liverpool fans thought Salah had won it in the penultimate minute but his shot ruffled the side-netting, with both teams left to settle for a point after a breathless festive treat.
Key Opta Stats:
- There have been 27 goals scored in the last five Premier League meetings between these teams (10 for Arsenal, 17 for Liverpool) at an average of 5.4 per game.
- Liverpool have scored 54 away goals in all competitions in 2017, their most in a calendar year since 1982 (66).
- Arsenal have conceded seven goals in two league games against Liverpool this season – in only one Premier League campaign have they conceded more against an opponent (10 v Man Utd in 2011-12).
- Since Jurgen Klopp's first Premier League match in charge in October 2015, Liverpool's games have seen 279 goals scored (174 for, 105 against), more than any other club.
- Phillipe Coutinho has been involved in 16 goals in 11 away matches across all competitions (nine goals, seven assists).
- Roberto Firmino has been involved in eight goals in his last five Premier League appearances against Arsenal (five goals, three assists).