With 46,811 tickets sold for the clash at Arsenal's Emirates Stadium, Chelsea's Zecira Musovic was the busier of the two goalkeepers, pulling off a string of superb reflex saves to keep her team in it as the home side dominated.
Arsenal took the lead when Chelsea's Niamh Charles conceded a penalty in the 56th minute by bundling over Caitlin Foord, and Kim Little rattled the spot kick past Musovic to break the deadlock.
Sweden's Musovic prevented a second for Arsenal, tipping a ball to the back post from Steph Catley onto the crossbar as Chelsea struggled in attack, not registering an effort on target until Magda Eriksson's tame header in the 77th minute.
The leaders looked to be headed for their second league defeat of the season before Australian Kerr spared their blushes, heading home from close range to grab a scarcely deserved point.
Everton moved up to fifth with a 3-2 win at home to Reading, while bottom side Leicester City grabbed their first points of the season with a surprise 3-0 hammering of Brighton & Hove Albion.
Chelsea top the standings on 28 points, three ahead of Arsenal, who have a game in hand over the Blues but who slipped to third when Manchester United rattled in six goals at home to Liverpool later on Sunday to go above them on goal difference.
On Saturday, former Chelsea striker Beth England netted on her debut for Tottenham Hotspur but ended up on the losing side as Kirsty Hannon set up both goals in a 2-1 win for Aston Villa.
