The home side made the perfect start when Bryan Felvus played a dangerous ball across the face of goal and Tommy Lennox was on hand to tap home at the back post.
Ten minutes later the same combination almost doubled Albion's advantage but on this occasion the woodwork denied Lennox.
Montrose were beginning to creep back into the match at this stage with Jered Stirling and Greig Henslee both forcing Jamie Ewings in the Albion goal to make some excellent saves.
In the 39th minute a Hugh Davidson header rebounded back off the post following a Stirling corner but, despite all the visitors' pressure, it was Albion that snatched a second goal.
Again it was some good work on the left by Felvus who played a neat ball into Chaplain who turned the last defender and fired the ball home.
Montrose did pull one goal back on 51 minutes when a defensive error by Kevin Nicoll let Henslee in on goal and he made no mistake as he fired a shot past Ewings.
Albion restored their two-goal advantage on 55 minutes when Phillip Creaney released Brian Smith down the left channel and his cross broke back to Creaney who drove the ball into the top corner.
The visitors piled the pressure on for the rest of the half as they looked to get back into the match but Albion held firm for the victory.