The Pirates saw Beardsley sent off in the 37th minute and Albion took full advantage thanks to a fiercely struck 25-yard effort from Robbie Weir just before the hour mark as Rowett's side got their promotion push back on track.
Rovers were reduced to nine men in added time when top scorer John-Joe O'Toole was given his marching orders, while the hosts also had winger Jimmy Phillips sent off by referee Paul Tierney for a second yellow card late on.
Rowett said: "We started brightly but got a little frustrated.
"Then, as we find so often, a sending-off changes a game.
"It's already happened to us this season and these things do tend to even themselves out.
"We possibly should have got a couple more goals and I thought we played quite well in patches.
"Once they were down to 10 men we tried to make the pitch as big as we could to stretch them.
"We also had a player sent off for what I thought were two fairly innocuous challenges. Unfortunately, in the modern game players have got to learn you just can't dive into a tackle.
"It's a shame because people see the physical side of football as part of the spectacle, but it is starting to go out of the game a little bit."
Rowett added: "Result-wise, it's nice to get back to winning ways after the defeats against Morecambe and Dagenham.
"We've got another a home game on Tuesday (against Mansfield) so it's a job half done."
- Sports & Recreation