Jordan Henderson had added to Luis Suarez’s 17thleague goal of the season to put Brendan Rodgers’ team in control at the hour mark.
In a grandstand finish, Arsene Wenger’s team went all-out for the winner but Liverpool remained resolute through a combination of grit, fortune and poor finishing from the hosts.
The draw meant that Arsenal remained four points behind fourth-placed Tottenham in the race for the Champions League positions.
It will agitate Wenger that his side has mustered only a single point in league fixtures against Manchester City, Chelsea and Liverpool this month after some more abject defending on a marquee occasion.
For Liverpool, Rodgers also rung the changes from the weekend, with skipper Steven Gerrard returning to the team alongside fit-again pair Pepe Reina and Glen Johnson, Daniel Agger, Lucas, Jamie Carragher and Stewart Downing.
It was like football in fast-forward in the early exchanges as the two teams traded lightning quick attacks and clear goalscoring opportunities.
Suarez, starting on the left of the three attacking midfielders behind central striker Daniel Sturridge, caused havoc with his uncanny ability at finding space, and also for some spectacular passes from out wide.
The Uruguayan’s goal owed much to some calamitous defending from the home side. Bacary Sagna's slip allowed Glen Johnson to run clear on the left and, after a hashed clearance from Thomas Vermaelen and a smothered shot from Daniel Sturridge, Jordan Henderson tapped the rebound to Suarez, whose shot deflected off a defender and in.
Arsenal responded by carving open Liverpool’s defense seemingly at will with some excellent combination play. The menacing Theo Walcott (twice) and Olivier Giroud both came close to scoring an equalizer.
Somehow, Liverpool held firm, although it had Gerrard to thank for an excellent last-ditch clearance that followed another zippy Arsenal attack.
Rodgers’ pre-match sermon appeared to have fired up the visitors, who were incisive in possession and pressed the hosts’ jittery defense into making mistakes as they ended the opening period the better team.
The one let-down was Henderson, who made a series of wonky passes when well placed. Yet, the midfielder kept getting in good positions and came close to doubling the visitors’ advantage with a chipped shot on the cusp of half-time that landed on the roof of the net with Szczesny stranded.
Following 15 minutes of second-half dominance from Arsenal, Henderson made another excellent run and finally made it count with a fine solo goal.
After turning past Per Mertesacker and outmuscling the substitute Andre Santos, the midfielder collected a lucky rebound after his first shot was saved to pass the ball into an empty net.
Arsenal were momentarily demoralised but were soon back in the game following two goals in three minutes.
The comeback began when Giroud headed in Jack Wilshere’s right-wing free kick for his fifth goal in three games and his 14thof the season.
But the best goal of the night came after 67 minutes, when Walcott, who had been lively all game on the wing, received a lay-off on the right side of the box and sent the ball flying into the far corner of the net with a shot of tremendous speed and precision.
Arsenal threw bodies forward as it went all out for the winner with some wonderful attacking play.
Giroud got in some excellent positions but was guilty of missing a hat trick of chances late on, including a sitter with only a few minutes on the clock.
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