Mikel Arteta's side trailed to first-half goals from Cody Gakpo and Luis Diaz at Anfield. But Gabriel Martinelli reduced the deficit before Mikel Merino grabbed the visitors' equaliser.
Although Merino was sent off for a second booking with 11 minutes left, Arsenal clung on for a vital point in the battle for a top-five finish in the Premier League. Second-placed Arsenal sit five points clear of sixth-placed Aston Villa.
They face a crucial clash with third-placed Newcastle at the Emirates Stadium next week before travelling to relegated Southampton on the last matchday.
With a vastly superior goal difference to all their top-five rivals, Arsenal should need just one more point to secure a Champions League berth despite winning only one of their last six league games.
Trent Alexander-Arnold was dropped to the bench by Liverpool boss Arne Slot, just days after the Merseyside-born England right-back confirmed he will leave.