Rovers started brightly, causing Newcastle plenty of problems, particularly down the left-hand side, through Steph Marsh, who was playing in a more advanced role.
Nichol Forster and Keeleigh Savage combined well up front, creating numerous chances, and a quick-fire Forster double put Rovers firmly in control.
Rovers added a third on 35 minutes when Zara Musker broke clear from right-back, before unselfishly squaring the ball for Savage to tap home.
Newcastle came back into the game as the half drew to a close and started the second half in a similar vein.
The visitors reduced the arrears on 52 minutes through Jessica Havelock’s stunning 30-yard strike and the goal gave them further encouragement to push forward.
Newcastle pulled a second goal back through Megan Pyper 15 minutes from time, but a resilient Rovers responded well and secured the win late on when Danni Young crossed for Marsh to score.
Manager John Prince said: “This was an important result for us on the back of three defeats. It was great that we were able to build on last week’s performance against Stoke and get a result to go with it.
“Amie Fleming and Steffi Hardy both came on for their first team debuts in the second half and it is exciting to see such a young team starting to gel together.
“Hopefully the win will give the girls some encouragement going into a tough game away to Nottingham Forest, who I expect to be one of the strongest teams in the league.”
ROVERS: Hutcheson, Musker, Middleton, Seed, McLellan (S. Hardy 65), Young, Flynn (Fleming 72), H. Forster, Marsh, Savage (Anderton 72), N. Forster.
Subs not used: Jackson, R. Hardy.