A Craig Bellamy brace and an Andy Todd header booked Rovers' place in the fourth round draw.
Rovers boss Mark Hughes made five changes to the side that defeated Portsmouth on Monday night, with 19-year-old Sergio Peter making his debut for the club.
And the young German winger's contribution was of the highest quality, setting up all three goals.
On three minutes David Thompson skipped away from two challenges before being fouled right on the edge of the box. Peter whipped a dangerous ball across the goal but it somehow eluded both the far corner of the net and the on rushing Bellamy's head.
Rangers who drew with Rovers' rivals Burnley earlier in the week, worked hard just to stay in touch, but struggled to make any real impression on the game.
Their biggest threat came from 37-year-old Paul Furlong in attack. On 11 minutes the former Chelsea and Birmingham striker almost capitalised on Todd's mistake, but his right-footed volley was comfortable for Brad Friedel in the Rovers goal.
Two minutes later and Furlong again made the most of some bad defending by the Rovers captain and after playing the ball through to his strike partner, Shabazz Baidoo, forced a smart save from Friedel, diving to his right.
But that was as good as it got for Ian Holloway's side, as Rovers' Premiership quality soon told. On 16 minutes Lucas Neill attempted to find Bellamy with a ball over the top, but after the Welshman miscued, Paul Dickov forced Simon Royce into a reaction save with a volley from 12 yards out.
And from the resulting corner Rovers were in front. Peter delivered the perfect ball deep from the right and Todd arrived unmarked at the back post to head the ball into the unguarded net.
On 36 minutes the home side was two ahead. Peter raced clear of his man down the left before picking out Bellamy on the edge of the box and the Welshman knocked home his eighth of the season with a left-footed volley that found the bottom corner of the goal.
The second half was something of an anti-climax as Rovers continued to hold the whip hand, before Bellamy put further gloss on the scoreline with just four minutes left to play.
Blackburn: Sergio Peter - The young German made a stunning debut by having a hand in all three Rovers goals to suggest that he has a bright future ahead of him.
QPR: Paul Furlong - The veteran striker was the spearhead for the Hoops and gave a fine all-round display that went unrewarded.