A fourth minute penalty from West Brom striker Tyler Roberts was enough to inflict a narrow defeat on Rovers at Aggborough.
Rovers had barely had a touch of the ball when keeper Andy Fisher felled Roberts in the box, which the forward duly converted.
That proved to be the only goal of a game that was high on energy and enthusiasm, but low on serious opportunities.
Rovers had the better of the ones that were created, but they lacked that cutting edge in front of goal.
Damien Johnson made just the one change to the side that picked up a point in a goalless draw away at Brighton seven days ago.
With Joe Grayson missing out through injury, his place in the centre of midfield was taken by Lewis Travis.
But the visitors had hardly got out of their own half from the kick-off when they found themselves a goal down after just four minutes.
A fine through ball saw Roberts in on goal only to be brought down in the box by Rovers keeper Andy Fisher and the striker picked himself up to send Fisher the wrong way to give the home side the lead.
It took Rovers a while to get into the game as they struggled with Albion's long ball, but as the half wore on it was they who started to impose themselves without ever really testing Jack Rose in West Brom's goal.
Set-pieces seemed to be the best chance of a way back into the game for Johnson's side. On 24 Joe Rankin-Costello was adjudged to have fouled the keeper from a Connor Mahoney corner kick, 90 seconds later a Mahoney free-kick was nodded on at the back post but Lewis Mansell couldn't force the ball home.
The Rovers forward then went close when he flicked on a centre from Matty Platt, but it deflected off a home shirt and behind.
Rovers continued to threaten as the half drew to a close. Lewis Travis doing well to play on despite being fouled to find Lewis Hardcastle who teed up Willem Tomlinson for a 20-yard shot, but his effort flew narrowly over the bar.
Albion were the livelier of the two sides at the start of the second half with a couple of breaks from deep, but like the first, once Rovers got into their stride it was they who were forcing the pace.
The visitors continued to play with good energy and enthusiasm, but despite a host of promising openings, they were unable to carve out a clear cut opening.
Joe Rankin-Costello was denied after breaking into the box, then a Mansell ball across the area deserved better as there was no man in red running in to fire home.
Connor Thomson and Dean Rittenberg were both introduced in the closing stages to add to their attacking threat and whilst play was firmly centred around the Albion box in the closing stages with a host of corner kicks, they were unable to grab the equaliser their play deserved.
WEST BROM: Rose, Wilson, McCourt, Donnellan, Fitzwater, O'Shea, Leko, Field (sub Barbir 89 mins), Roberts, Tayki (sub Sweeney 85 mins), McManaman.
Subs not used: Harper, Palmber (GK), Elbouzedi.
Goals: Roberts (pen) 4 mins.
Booked: Field (41 mins).
ROVERS: Fisher, Nyambe, Doyle, Travis, Platt, Wharton (c), Mahoney, Tomlinson, Mansell, Hardcastle (sub Rittenberg 76 mins), Rankin-Costello (sub Thomson 67 mins).
Subs not used: Howarth, Powell (GK), Magloire.
Booked: Fisher (3 mins), Travis (50 mins)