Gilberto was dismissed for kicking Robbie Savage as early as the 13th minute, but goals in each half from Kolo Toure and Thierry Henry secured a seventh win in nine games for Arsene Wenger's side.
Rovers made five changes to the side that swept aside Everton 4-1 in the FA Cup last weekend, with Benni McCarthy, Savage, Stephane Henchoz, Brett Emerton and captain Lucas Neill all returning to the starting line-up.
Arsenal arrived at Ewood Park on the back of successive cup victories over Liverpool, scoring nine goals in the process, but Wenger kept faith with only three of his young stars from Tuesday's 6-3 win at Anfield - Toure, Cesc Fabregas and Justin Hoyte the trio to make the grade.
Buoyed by six victories in their last seven games, Mark Hughes' side began the proceedings brimming with confidence.
On ten minutes, Morten Gamst Pedersen picked out the unmarked Matt Derbyshire with an inswinging corner from the right, but the striker put his free header inches wide of Jens Lehmann's right-hand post from four yards.
Three minutes later and Rovers were given another major boost when the Gunners were reduced to ten men. Savage put Gilberto under intense pressure in the middle of the park, the Brazilian kicked out at the Welshman and was duly sent for an early bath by referee Rob Styles.
Rovers continued to force the pace and again threatened the Arsenal goal on 23 minutes. After Emerton's mazy run from right to left, the Australian slipped the ball through to Pedersen, whose fierce drive was tipped over the bar by Lehmann.
But against the run of play, the visitors took the lead. On 36 minutes, Neill brought down Robin van Persie, after giving the ball away, and from the resultant Henry free-kick, Toure rose above his marker to head the ball off the inside of the near post and into the back of the net.
Rovers were almost back on level terms just two minutes later, but Savage's downward header, from Andre Ooijer's cross, bounced agonisingly wide of the mark.
Tugay was brought on for Aaron Mokoena at the break, as Rovers made a positive start to the second half. On 58 minutes, Neill slipped the ball through to McCarthy, but with bodies to pick out in the centre, the South African opted for a shot at goal and could only pick out the side netting.
On 65 minutes, Pedersen supplied another pin-point cross from the left, but substitute Shabani Nonda's header sailed high over the bar.
Two minutes later and again Rovers came close. Neill made an incisive run into the box, before picking out Derbyshire at the back post, but with virtually an open goal to aim at from less than two yards, the forward couldn't direct his volley on target, arriving at the back post at full stretch.
And the home side were made to pay for the string of missed chances, as the Gunners sealed the win with trademark quick break.
On 71 minutes, a Rovers free-kick was cleared down the left to Henry and after galloping fully 40 yards forward, the Frenchman played a neat one-two with Fabregas, before curling the ball into the top right-hand corner of Brad Friedel's goal from the edge of the box.
The Arsenal captain ought to have grabbed a second minutes later as Rovers threw bodies forward, before he was brought off to a standing ovation from the entire crowd late in the game.