Despite dominating the first half, Rovers trailed 1-0 at the break.
Rovers recorded 13 chances in the opening period, but their profligacy in front of goal again proved costly, as Albion caught the visitors napping on 36 minutes - Kayleigh Griffiths getting the goal.
After a stern talking to at half-time, Rovers responded with the equaliser within 26 seconds of the restart. Vicky Westerman did all the hard work, before Keira Walsh unleashed an unstoppable shot from the edge of the area.
The two teams battled it out in the second half, with Rovers substitute Nicky Emery twice denied late on when one-on-one with the Albion keeper, as both sides had to settle for a share of the spoils.
Interim manager Gemma Donnelly said: •Up until 33 minutes, Albion couldn't get out of their half, we totally boxed them in, and I felt that we were on course for a decent three points.
"Towards the end of the game, I would have taken a draw. It's a good point for us. It moves us out of the relegation places, albeit on goal difference, and we've got a huge game at the weekend against Leeds.
"On the back of the victory away to Derby County and the performance against Preston in the Lancashire Cup final, it was another good team display.
"It's no coincidence that since the inclusion of Amanda Goodwin into the team, results and form have picked up. She adds that quality into midfield and whilst I appreciate it's difficult for her to be player-coach, for the purpose of pulling us out of a difficult situation, her hard work epitomises what the club stands for."
ROVERS: Hutcheson, Fleming, Savage, Seed, Bourne, Flynn, Goodwin, Walsh, Westerman (H. Forster 81), N. Forster, Adams (Emery 58).
Subs not used: Barratt.