Recent signing Amy Botfish netted her second hat-trick in as many games, whilst Lili-Beth Bown opened and closed the scoring, as Stour overcame a Rugby outfit who had caused them problems in both previous League meetings this season.
Rugby started the stronger, with more of the play in the opening minutes, but Stour were soon into their stride, and it was no surprise when Bown sliced her way through the visiting defence to give the Glassgirls the lead, before Botfish's emphatic finish doubled that advantage shortly afterwards.
Botfish should have made it three when clean through but a heavy touch as she rounded the Rugby keeper saw the ball get away from her. However, there was no mistake from a similar position when she elected to shoot first time, the ball finding the far corner of the net.
The visitors kept things interesting as the interval approached as some slack defending saw Paige Bennett exposed in goal, and beaten with a cool finish, and Stour looked briefly unsettled and glad to see the break.
Botfish and Bown both saw chances go wide early in the second half, but there was no mistake from Botfish as she made it 4-1, slipping the ball under the keeper from close range.
Stour could have added more goals with a little more composure in front of goal, and they were thankful to Bennett for a fine diving save from a direct free kick as Rugby looked for a way back into the game.
However, the impressive Bown had the final word as she got the slightest of touches with her head to a free kick from Jo Cornford to round off the scoring.
In Sunday's other quarter final, Coventry Sphinx gained a surprise 3-0 win at Gornal, whilst the other ties (Coventry Development v Droitwich Spa and Solihull Sporting v Solihull United) were both postponed.