Andy Todd was sent off for a controversial handball in between goals from James McFadden and Mikel Arteta on Everton's four thousandth game in the top-flight.
Mark Hughes made three changes to the side that dramatically dumped Charlton out of the Carling Cup on Wednesday night.
Lucas Neill and Tugay returned from injury and, after his goal of the season contender, David Thompson was rewarded with his first start of the campaign.
Everton made one change from the side that beat Newcastle the previous weekend, Leon Osman coming in for the suspended Tim Cahill.
And after scoring three goals in a frantic final 15 minutes in midweek, Rovers looked to continue where they had left off.
In the third minute, and after a well worked break down the right, Thompson did brilliantly to cross the ball into the box. Steven Reid let it run through his legs and the unmarked Morten Gamst Pedersen ought to have hit the target six yards out.
Seven minutes later and the Norwegian winger went close once again. Following an incisive run through the centre, Craig Bellamy played in Pedersen to his left, but his delicate lob to the far post struck the upright and was cleared to safety.
The subsequent 20 minutes saw the game go through a sustained low, but as Rovers looked to be in control, they suffered a double blow in a dramatic two-minute spell.
A long ball forward was bravely flicked on by Andy van der Meyde and McFadden raced ahead of Michael Gray to head past a helpless Brad Friedel.
Moments later, and with Rovers in disarray, Andy Todd found himself one-on-one at the back and as former Rover James Beattie looked to go past him, the ball struck the arm of the Rovers skipper and after consulting his linesman, referee Mark Halsey produced a straight red.
From the resulting free-kick Arteta came within a whisker of making it two, however the visitors didn't have to wait long until they doubled their advantage.
In the 45th minute, after Tugay and Beattie tangled, the ball broke kindly for Osman, who played it square to Arteta and the Spaniard coolly picked out the top corner from the edge of the box.
Both sides made changes at the break, Richard Wright replaced Nigel Martyn in the Everton goal and Zurab Khizanishvili came on for Thompson as Rovers were forced to reshuffle their pack.
It was the home side who began the half brightly, Pedersen again going close with a free header at the back post less than three minutes in.
Ryan Nelsen almost capitalised on a goalkeeping error, before Tugay unleashed a trademark volley that almost found the top corner from 25 yards.
The Ewood Park crowd watched on with hope more than expectation of another Rovers comeback, but the threat of an Everton counterattack and a host of substitutions and needless bookings were all a lacklustre second half had to offer.
Man of the Match: Joseph Yobo - The Nigerian defender was a rock in the Toffees backline and ensured that the Rovers attack were kept on a tight leash.