In a game in which there was little between the two sides, a goal six minutes before half time from Albion striker Alex Jones settled the match.
In blustery conditions at Albion's training ground it was Rovers who had the first meaningful chance of the game on 9 minutes.
A Fabio Nunes free-kick was floated into the area but trialist Aaron Tumwa headed over when well placed.
Rovers continued to force the pace with Tim Payne letting fly from distance, the ball flashing a yard over the bar.
Rovers gave a second runout of the summer to defender Adam Henley and he almost teed up Bradley Orr for the opening goal but the full back volleyed just wide from inside the area.
Fabio Nunes saw a free-kick tipped over the bar before the Portuguese winger squeezed a shot narrowly wide in a crowded penalty area.
However despite Rovers creating the better chances it was the home side who took the lead on 39 minutes.
A goalbound cross into the area from Kemar Roofe was tipped away by David Raya in the Rovers goal but Alex Jones reacted the quickest to nod home from close-range.
The start of the second half should have seen the Baggies double their lead. Aaron Birch saw his shot blocked but Morgan Ferrier fired the rebound high over the bar when it seemed easier to score.
The second period was a tighter affair as both sides struggled to cope with the windy conditions on the exposed pitch. Rovers defender Kellen Daly seeing a header claimed easily from a Raheem Hanley corner kick, in a rare attempt at goal.
Rovers made changes in a bid to get back into the game with striker Deniz Pero and Under-18 midfielder Ian Vicars coming on.
The final few seconds saw a flurry of chances, firstly David Raya made a fine double save to deny Jones and Birch in quick succession, before good play down the left saw Ian Vicars find Jordan Preston but his first-time shot was weak and easily saved.
Eric Kinder's Under-21s are back in action next Monday when they take on Reading at Ewood Park.
ROVERS: Raya, Orr, Henley (sub Vicars 60 mins), Paulo Jorge (sub Pero 77 mins), Daly, Tumwa, Fabio Nunes, Payne, Preston, Bauress, R. Hanley.
Subs not used: Urwin, Haley, Paul.