The hosts controlled much of the contest but could not find the finishing touch until captain Kim Little fired home from the spot on 57 minutes.
Steph Catley’s second-half effort from distance hit the crossbar and the Gunners, who were largely the dominant side, looked set to seal the points but the resilient Blues came alive in the final minutes.
Chelsea remain three points clear of Arsenal, who have a game in hand, at the top of the WSL table.
Frida Maanum tested Zecira Musovic with an early cross from the right corner before Stina Blackstenius mirrored her effort from the right, both attempts easily handled by the Chelsea shot-stopper.
Chelsea survived a wave of Arsenal attacks and the ball fell to Lauren James, who drove down the right channel and into the area and sent a strike from the centre wide of Manuela Zinsberger’s left post.
Arsenal threatened when Blackstenius won the ball in midfield and flicked a neat pass to Lina Hurtig at the edge of the area, who managed to direct the ball through two blue shirts but Musovic was there to make the stop.
Musovic was soon called into action again, first thwarting Caitlin Foord then leaping to deny Maanum from opening the scoring with a strike from the right.
Chelsea found a brief foothold but the opening 20 minutes were controlled by the hosts as Maanum fired another low, sharp effort between two Blues and into the path of the awaiting Musovic.
Kadeisha Buchanan did well to prevent the initial threat from another wave of attack with two vital blocks in quick succession but the ball remained in Chelsea’s half. The Gunners wasted a corner, then an onrushing Hurtig latched onto a pass from Maanum but sent her attempt from a tight angle into the side netting.
The sides remained goalless at the break during which former Arsenal stalwart Jordan Nobbs, who this month signed for Aston Villa, was on the pitch for a farewell after 12 years as a Gunner.
The second half started largely as the first one ended as the hosts re-asserted themselves, Zinsberger blocking Hurtig’s curling effort from the right, and getting her body in front of the Sweden international’s attempt to head home from close range soon after.
Arsenal finally took the lead when Niamh Charles brought down Foord as she drove down the left and referee Emily Heaslip pointed to the spot. Skipper Little stepped up and fired into the right corner.
The hosts were inches away from doubling their lead when Catley unleashed an effort from distance, Zinsberger appearing to get her fingertips on the ball before it pinged off the crossbar.
Chelsea substitute Jelena Cankovic made a near-instant impact, sending a long ball into the area for Kerr to neatly nod home in the 89th minute and snatch a precious point.