Rovers' record goalscorer reached the memorable milestone shortly before the break, whilst Rio Hardy bagged a second-half hat-trick to help secure Rovers' semi-final spot.
The visitors dominated from the off and eventually broke the deadlock on 40 minutes when Anderton lobbed the goalkeeper.
Gemma Jackson made a magnificent reaction save at the start of the second half to preserve Rovers' lead and from then on it was one-way traffic.
Danni Young grabbed her third goal in the competition and Hardy hit a hat-trick as Rovers eased into the next round.
Interim manager Gemma Donnelly said: "We retained possession for long periods and we had to be patient, but once we clicked, they tired and our quality shone through.
"All credit to Blackburn Community Sports Club for giving us such a challenge and for their hospitality on the day.
"A special mention also to Amie Fleming, who was outstanding at left-back, and Chloe Adams, who made a massive difference after coming on. She provided plenty of energy down the left-hand side and was positive in her play. Gemma Jackson also stepped up to the plate when called upon."
ROVERS: Jackson, Musker, Seed, S. Hardy, Fleming, Young, Flynn, H. Forster (Bland 75), Anderton, N. Forster (Adams 55), R. Hardy (Noori 75).
Subs not used: Hutcheson.