Rovers made the worst possible start, conceding twice in the opening five minutes.
On two minutes, Rovers were caught napping, as they didn’t react to a ball over the top, which the lively Abbie McIver latched onto before firing home.
Moments later, Felicity Middleton under hit a back pass to Jo Hutcheson, who came rushing off her line to make a brilliant block from Emma Bentley, but the ball ricocheted back off the striker and into the unguarded goal.
Rovers battled back, creating numerous chances and putting Leeds under pressure. Midway through the half, Nichol Forster was brought down in the box and Katie Anderton made no mistake from the spot.
Rovers remained on the front foot, with Danni Young supplying an excellent cross from the right for Anderton, who rose above her marker, but headed over the bar.
The hosts then wasted a golden opportunity to get back on level terms, as Anderton pinched possession and rounded the keeper, but fired over the bar from the edge of the area with the goal gaping.
The chances continued to come Rovers’ way after the restart, as Nichol Forster headed over the bar and both Anderton and Young struck the side-netting.
Rovers were made to pay, as McIver scored her second goal of the game midway through the second half.
Rovers responded by bringing on Amy Bland, who pulled a goal back late on when she converted a cross at the back post.
John Prince’s side pushed for an equaliser, but were beaten by the clock.
“We got off to a really bad start, which put is in a really difficult position,” said the manager.
“We’re disappointed and frustrated by the result. Despite it being a close game, we really felt we should have done better.
“The players need to understand that if we don’t perform well in what is a competitive league, we’re not going to get positive results. Overall, it was a below par performance, but we are determined to bounce back away to Bolton in the Lancashire Cup this weekend.”
ROVERS: Hutcheson, Musker, Middleton, Seed, McLellan, Young, H. Forster (Savage 46), Fleming, Marsh (O'Donnell 60), Anderton, N. Forster (Bland 70).
Subs not used: Jackson, R. Hardy.