After a goalless first half, in which Rovers were the better team, second-half strikes from Kirsty Allen and Stephanie Smith secured the points for Forest.
Rovers started strongly and almost opened the scoring inside the first minute when Katie Anderton turned sharply and shot, but the goalkeeper did well to tip the ball over the bar.
John Prince’s side continued to apply pressure, keeping Forest on the back foot, with Danni Young and Steph Marsh causing problems down the flanks and Amie Fleming providing a physical presence in centre midfield.
Rovers won a number of corners, which they came close to converting on a couple of occasions.
The visitors were made to pay for their profligacy in front of goal, as Forest made the breakthrough just three minutes after the interval when Trina Greaves played a superb ball through to Allen, who calmly slotted past Jo Hutcheson.
The Scottish stopper made a couple of fantastic full-stretch saves to keep Rovers in the game at 1-0 and they were almost rewarded, as Kelly McLellan volleyed over from close range and substitute Rio Hardy had a header cleared off the line.
However, moments later, Forest wrapped up the win when the ball dropped to Smith on the edge of the box and the midfielder hit a first-time half-volley into the roof of the net.
Manager John Prince said: “It was a very close and competitive game, played in good spirit.
“I felt that we were the better team in the first half and should have been ahead at half-time. They were better in the second half and scored two good goals.
“It’s disappointing because on another day we could have won the game, but we didn’t take our chances. I’m very pleased with the level of performance, particularly the work rate and attitude the team showed. It was certainly a vast improvement on our last away game at Sheffield, which we lost 7-0.
“However, as a coaching team, whilst we are pleased with the efforts of the players, we don’t just want to settle for working hard and being competitive. We need to focus on being more clinical when the chances arrive, so that we can come away with the points.”
ROVERS: Hutcheson, Musker, Seed, Middleton, McLellan, Young, H. Forster, Fleming (Bland 72), Marsh (Savage 72), Anderton, N. Forster (R. Hardy 60).
Subs not used: S. Hardy.