The record goalscorer, who was presented with a commemorative shirt at Ewood Park on Saturday to mark a memorable milestone, netted her 201st goal in Rovers’ colours 20 minutes from time to secure three precious points for Gemma Donnelly’s side.
Both teams made a scrappy start to the contest, as they struggled to find their feet. Rovers grew into the game as the half progressed, looking particularly dangerous on the break.
Anderton played in Rio Hardy, who was denied by a last-ditch tackle, before Danni Young and Nichol Forster both fired over in one-on-ones.
Rovers restricted Albion to just one clear chance of note, but goalkeeper Gemma Jackson was alert to make a smart save.
The hosts came flying out of the blocks at the start of the second half, putting Albion under plenty of pressure.
Substitute Steph Marsh ought to have done better, but the ball got stuck under her feet, before Anderton again slipped in Hardy, whose strike clipped the top of the crossbar.
Young and Amie Fleming then combined well down the right, before Nichol Forster found Anderton in the area, but after turning the defender, she shot straight at the keeper.
The breakthrough eventually arrived with 20 minutes remaining. Following a long ball forward by Helen Seed, an Albion defender dallied in possession and was robbed by Anderton, who coolly slotted past the keeper into the bottom corner.
The hosts had further opportunities to put the game to bed, but lacked a cutting edge in the final third and a resolute Rovers rearguard had to withstand some late pressure from the visitors to secure a first league victory since September.
Assistant manager Amanda Goodwin said: “It was a well-fought team effort and a thoroughly deserved three points. The scoreline doesn’t reflect our superiority. We created countless chances, but didn’t capitalise on them.
“Everyone gave 100% and we were in complete control of the game throughout. The girls showed great character to keep the scoreline at 1-0 when Albion pushed for a late equaliser. There is a determination to work hard and a real togetherness in the squad at the moment, which is great to see.
“We go into the cup game against Sporting Club Albion on a high now and it is important we take the positives from Sunday’s performance into that game.”
ROVERS: Jackson, Fleming, Seed, S. Hardy, Bourne (Marsh 37), Westerman (Flynn 60), H. Forster, Anderton, Young, N. Forster, R. Hardy.
Subs not used: Noori.