The home side battled back from a goal down to claim a 3-1 triumph at the Academy Stadium, thanks to a Bunny Shaw brace and Vicky Losada strike.
The Robins had forced an opener via an Alex Greenwood own-goal but City responded superbly to turn the game on its head before half-time, sealing the tie with Losada's effort shortly after the hour.
The game was shown live on CITY+ and featured co-commentary from City defender Esme Morgan - fresh from signing her new contract!
CITY V ARSENAL
Tickets for City's first home league game of 2022 - a crunch FA WSL clash against Arsenal - are now on sale.
Don't miss your chance to cheer on Gareth Taylor's side on Sunday 23 January. Kick-off 18:45 at the Academy Stadium.