Kerr latched on to a long ball from keeper Zecira Musovic and fired home in the second minute of added time before wheeling away and taking off her shirt in celebration as second-placed Chelsea kept up the pressure on leaders Arsenal.
The match was played against an uncertain backdrop given Roman Abramovich's alleged ties to Russia President Vladimir Putin.
The Premier League disqualified owner Roman Abramovich on Saturday after the United Kingdom government sanctioned him in the wake of Russia's invasion of Ukraine.
It left the club facing a string of stringent regulations to adhere to, including the closure of the club shop, inability to sell merchandise or offer new contracts to players.
The result puts the Blues on 35 points, five behind Arsenal and with two games in hand.
Bottom side Birmingham City took a step closer to the drop when they lost 1-0 at home to West Ham United, while fifth-placed Manchester City kept up their chase for a Champions League spot with a 1-0 win away to Tottenham Hotspur, who are fourth.
On Saturday, Leah Galton scored twice as Manchester United put in another fine performance and cruised to a 3-1 win away to Reading.
On Merseyside, Swede Anna Anvegaard struck twice to give Everton a 3-2 win at home to second-from-bottom Leicester City, a result that leaves Everton ninth in the 12-team league.