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We dominated the first 45 minutes but couldn't make our chances count, with Lisa Baum and Kyra Cooney-Cross going closest to breaking the deadlock.
Despite our dominance, it was the visitors who struck first on the counter-attack through Oceane Hurtre, before Olivia Smith equalised with a stunning effort from 20 yards.
We started on the front foot at Emirates Stadium and had our first chance just five minutes in when Alessia Russo's effort from the edge of the penalty area was deflected just wide of the post.
Our main threat in the first half came from the wings, with Smith and Baum continuously beating their full-backs to the byline. Five minutes after our first chance, Baum's cross caused a scramble in the six-yard box, with the Blues narrowly escaping the danger.
We threated again when Smith broke free just before the half hour mark and picked out Stina Blackstenius, but the Sweden international couldn't hit the target with her near-post effort.
In what was our best spell of the opening 45, Cooney-Cross tested Sophie Baggaley from distance, with a well-struck drive towards the bottom corner, before coming close again from the resulting set piece as her low, driven effort was deflected wide of the post.
Our best chance of the half came when a sensational cross from Leah Williamson was met by a diving header from Russo, only for the post to deny us a first-half lead.
Smilla Holmberg had the first chance after the break, shrugging off a foul to force her way in on goal before firing a powerful effort just over the crossbar.
Having failed to capitalise on our opportunities, we were punished moments later. Hurtre charged away on the counter-attack, drawing out Misa Rodriguez and flicking a tidy finish into the bottom corner to give the visitors a smash-and-grab lead.
Ten minutes after falling behind, Ona Batlle's teasing cross to the far post was met by Baum, but her close-range header was kept out by a fantastic, point-blank save from Baggaley.
We weren't to remain behind for long though, as Smith took matters into her own hands and hammered a stunning strike into the top corner from 20 yards out to draw us level.
Chances continued to flow for us after the equaliser, and we would've had the lead with 15 minutes to play had it not been for a stunning save from Baggaley to deny Lotte Wubben-Moy after she latched onto Holmberg's excellent free-kick delivery.
Our WSL campaign continues with the first north London derby of the season, as we make the short trip to the Tottenham Hotspur Stadium to face our old rivals.
It'll be another 12.45pm kick-off for our Gunners on Saturday, October 17, and you can get your tickets for the derby here.