Midfielder Jessie Fleming scored after 66 seconds to set Chelsea on course for a 4-0 thrashing of Manchester City in the Women's Super League on Sunday, their first win away to City in the league, that keeps them second in the table.
Fleming pounced on a loose pass from keeper Karima Benameur to open the scoring, and Sam Kerr added a second in first-half stoppage time, with Fran Kirby and Magda Ericsson both scoring after the break as City's defence collapsed.
Bottom side Leicester City looked set to secure their first point of the season, but substitute Maisie Symonds struck a super free kick in second-half stoppage time to snatch a 1-0 win for Brighton and Hove Albion.
Reading also scored a stoppage-time goal to snatch a 2-2 draw away to West Ham United, while Birmingham City's poor start to the season continued as they lost 1-0 in their derby with Aston Villa.
Manchester United slumped to a 1-1 draw against Everton as forward Ella Toone's early goal was cancelled out by Simone Magill.
On Saturday, Arsenal dropped their first points of the season as they were held to a 1-1 draw by North London rivals Tottenham Hotspur.
Arsenal top the standings on 19 points after seven games, with Chelsea second on 18 and Brighton third on 15. Leicester remain bottom, with Birmingham City above them on one point.