Brazilian forward Kerolin struck a first-half opener for City and Dutch attacker Viviane Miedema added a second in the 63rd minute to secure the win, with Everton goalkeeper Courtney Brosnan pulling off a string of fine saves to keep the score down.
Reigning champions Chelsea, who have won the last six league titles, made the most of a litany of defensive errors by their visitors en route to a comfortable 5-0 victory that had Sandy Baltimore scoring twice.
City top the standings on 33 points with Chelsea, who dropped seven points in a nightmare three-game spell in November and December, second on 27 points.
Title hopefuls Arsenal and Manchester United played out a 0-0 draw in London on Saturday, as the two sides lost ground on the top two. Arsenal are third on 23 points and United fifth on 22.
Tottenham Hotspur climbed into fourth spot, behind Arsenal on goal difference, with a 1-0 win over Leicester City as a goal from a corner that appeared to go in off former Spurs defender Ashleigh Neville gave her old team the three points.
Encouragingly for Spurs, 20-year-old Signe Gaupset was superb on her debut after signing from SK Brann in her native Norway, picking up the player of the match award after an impressive display that lasted just over an hour before she was replaced.
Aston Villa came back from a goal down to beat Brighton & Hove Albion 2-1 at home, while Liverpool missed the chance to climb off the bottom of the standings after being held to a scoreless draw at home by London City Lionesses, who are seventh in the 12-team table.
The point gained was only Liverpool's fourth of the season and sees them remain in the automatic relegation spot, one point behind West Ham and four behind local rivals Everton, who are 10th.