First-half goals from Taylor Reynolds and Seren Watkins were enough for the Baggies to see out their opponents from a division lower.
Reynolds’ header on the half-hour-mark eased worries about the cagey opening to the match, before Watkins volleyed a Stingers clearance into the top corner.
Second-half efforts from Emma Bradley and Phoebe Warner were denied by the Cheadle goalkeeper, while an injury to Albion keeper Anna Miller at the close of the match saw Hannah George don the gloves.
**Birmingham City** are out of the competition after losing to Championship title-race rivals Durham 1-0.
Blues struggled to find a clinical edge and Wildcats’ Grace Ayre’s finish means City won’t be going into the fourth round.
**Aston Villa** struggled in the Super League against a strong Arsenal side, with the 4-0 loss leaving Villa ninth. England Internationals Alessia Russo (two) and Beth Mead scored, alongside Stina Blackstenius.
In the National League Northern Premier, **Sporting Khalsa** triumphed with a 6-1 win against Halifax.
Khalsa were 5-0 up at half-time, with goals from Megan Cann, Annabel Davies, Macy Winters and a brace from Laura Smith setting the scene early on.
Halifax pulled one back after the break, but late substitute Molly Philpott scored with a minute to go to seal the win.
**Hednesford Town** also enjoyed a dominant display away to Rugby Town, winning 5-1 in the West Midlands Division One North fixture.
Hazzana Parnell bagged a brace, as she was joined on the scoresheet by Amelia Lightfoot, Laura Sears and Leigh Dugmore.
**Lichfield City** beat league leaders **Walsall Wood** 4-2 thanks to goals from Courtney Dilger (two), Shelbie Cartwright and Dolcie Sims. Sophie Rowlands and Rosie Hargreaves scored for Wood.