Paul Dickov's seventh minute header saw Bolton Wanderers lose the sixth consecutive game and fourth at the Reebok - their worst sequence of results in the Premiership.
For Rovers, the three points were a fitting reward for a resolute defensive performance with central defenders Andy Todd and Nils-Eric Johansson outstanding, while in midfield, they were ably marshalled by captain Barry Ferguson.
Dickov added to his good show with a performance that kept Wanderers at full stretch, while the home side could only find comfort in the industry of Kevin Davies and the hard work of Jay-Jay Okocha and Ricardo Gardner.
Both sides could have had a goal in the opening minute.
Jay Bothroyd went clear after Gardner misjudged the bounce of the ball and Jussi Jaaskelainen did well to block the shot, while at the other end Davies tried to tee up El Hadji Diouf inside the area only to be foiled by the outstretched leg of Dominic Matteo.
As it was, there were only seven7 minutes on the watch when Rovers took the lead. Johansson pushed the ball forward where Bothroyd shepherded it to Dickov, who fired into the top corner from just outside the area.
Wanderers stepped up the tempo and created two chances that could have brought them the equaliser. First, Okocha's teasing cross into the six-yard box was beaten out with Stelios waiting to pounce, before Davies floated the ball to the far post where Henrik Pedersen volleyed just wide.
It was the Wanderers defence however that was causing concern after basic errors put their goal under threat. Rovers almost capitalised on this on the 35th minute when Jon Stead got clear of his marker only to head Garry Flitcroft's cross against the bar.
Yet Wanderers should have been level in first-half stoppage time, Diouf's cross finding Pedersen unmarked in the six-yard box, but the Dane headed straight into Brad Friedel's arms.
Wanderers started the second half with a strong penalty claim after Davies went down on under the challenges of two defenders.
That led to some spirited play from the Wanderers attack, but apart from a wayward volley by Davies, the Rovers defence, with Todd a commanding figure, were well in control.
The home side continued to have the major share of possession but lacked the invention to open up the way to goal, while Rovers always look dangerous on the break.
The Trotters, who had already bought on Ricardo Vaz Te for Pedersen replaced Gary Speed with former Real Madrid captain Fernando Hierro and Stelios with veteran striker Les Ferdinand.
However, it was the hard-working Davies, who almost got Wanderers back into the game, but his header from a Diouf corner flew narrowly wide.
Rovers were disappointed not to have confirmed their victory in stoppage time when Steven Reid fired the ball wide from a good position.