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The England international's double took her tally for the season to seven as Gareth Taylor's side made it five wins in a row in all competitions.
Stanway opened the scoring after five minutes when she received a pass from Ellen White and rifled in via a deflection.
It was 2-0 thanks to a superb team goal in the 40th minute. Lucy Bronze found White with a through-ball and the England forward again turned provider with a low cross that was converted by Vicky Losada.
The points were wrapped up with 16 minutes left when in-form Stanway tapped in at the back post.
After a difficult start to the campaign for the 23-year-old, including a sending-off against Manchester United, the attacker has now scored in five consecutive games to help City sit fifth in the table.
Manchester United Women moved up to third after they picked up where they left off before the winter break with a 5-0 thrashing of Birmingham Women.
Marc Skinner's side were playing their first match since December 19, when they put five past Villa, and repeated the trick with a scintillating first-half display.
Captain Katie Zelem chipped United ahead after 12 minutes and a quick-fire double from Leah Galton made it 3-0.
There was still time for another before the break as Ella Toone's effort hit the crossbar and rebounded in off goalkeeper Emily Ramsey for an unfortunate own-goal.
Alessia Russo wrapped up the scoring in the 71st minute when she headed home her fifth goal of the campaign to bring City back down to earth after last weekend's shock victory over Arsenal.
United climbed above Tottenham, who host West Ham on Sunday, while Birmingham remained in 11th position, a point above the solitary relegation spot in the league.