The Gunners lead on a perfect 18 points from their six games and are ahead of Chelsea on goal difference, while United slip to third spot on 15 points.
Striker Sam Kerr (29) scored on the hour mark after Millie Turner (26) passed the ball straight to Chelsea's Sophie Ingle (31) who played in Australia international Kerr for a controlled finish to break the deadlock.
Minutes later Kerr turned provider, sliding the ball into the path of Lauren James (21), who scored with a first-time finish before Alessia Russo (23) pulled one back for United to set up a grandstand finish.
However, rather than snatch an equaliser, United conceded a third as Erin Cuthbert (24) fired home a deflected shot in stoppage time to wrap up the three points for the Blues.
Earlier in the day, Brighton & Hove Albion scored five goals but barely managed to hang on for 5-4 win away to West Ham United, with Viviane Asseyi (28) grabbing two late goals for the home side.
Reading defender Emma Mukandi had a day to forget, scoring two own goals in eight minutes as her side lost 3-0 at home to Manchester City to leave them second from bottom in the table.
Liverpool's poor run of form continued with a fifth straight defeat as a Rachel Daly (30) penalty just before the hour mark gave Aston Villa a 1-0 win over the newly-promoted side, whose only victory this season so far came in their opener against Chelsea.
Tottenham Hotspur's home game against Everton was postponed due to a waterlogged pitch.
