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The visitors took an early lead when Joel Lynch put the ball into his own net after Matt Ingram had saved Sam Gallagher's header.
Liam Feeney tapped home from close range to double the Rovers lead before Jake Bidwell pulled one back from the penalty spot after Yeni Ngbakoto was fouled in the area.
Jordan Cousins had a chance to equalise for the hosts but shot wide late on.
Blackburn have now progressed to the fourth round for three successive seasons.
QPR, who have won their last two in the league, pushed for a late leveller but have now been beaten at the third round stage 48 times in their history - an unwanted record they jointly hold with Plymouth.
QPR boss Ian Holloway:
"That team, who haven't played before, will never be picked again. Simple as that.
"I wanted that team to fight and do it for each other. Unfortunately they couldn't do it.
"Simple things we don't do well enough as a group. It's very disappointing.
"There will be changes. You've got to get your foot in and we didn't do it well enough. Jamie Mackie did - he tackled everybody. But where's the rest? Come on.
"I've made some changes but I wanted to win and I thought that was a strong enough team."
Blackburn boss Owen Coyle:
"I always say that at the top end of the pitch you want players who can influence games by having assists or scoring goals, which is the best thing in the game.
"We say to wide players that they've got an onus on them to get in there and score goals. You can never have enough goalscorers at your club.
"So it was great that Liam Feeney got on the end of that and he earned it because his performances have been of a very high standard."
Match ends, Queens Park Rangers 1, Blackburn Rovers 2.
Second Half ends, Queens Park Rangers 1, Blackburn Rovers 2.
Corner,  Blackburn Rovers. Conceded by James Perch.
Substitution, Blackburn Rovers. Wes Brown replaces Sam Gallagher.
Foul by Joel Lynch (Queens Park Rangers).
Anthony Stokes (Blackburn Rovers) wins a free kick in the attacking half.
Ben Marshall (Blackburn Rovers) is shown the yellow card for a bad foul.
Jordan Cousins (Queens Park Rangers) wins a free kick on the left wing.
Foul by Ben Marshall (Blackburn Rovers).
Attempt missed. Jordan Cousins (Queens Park Rangers) right footed shot from the centre of the box is close, but misses to the right.
Substitution, Blackburn Rovers. Anthony Stokes replaces Danny Graham.
Corner,  Blackburn Rovers. Conceded by James Perch.
Substitution, Queens Park Rangers. Jordan Cousins replaces Massimo Luongo.
Attempt missed. Ben Marshall (Blackburn Rovers) right footed shot from outside the box misses to the right.
Foul by Massimo Luongo (Queens Park Rangers).
Ben Marshall (Blackburn Rovers) wins a free kick on the left wing.
James Perch (Queens Park Rangers) wins a free kick in the attacking half.
Foul by Danny Graham (Blackburn Rovers).
Foul by Joel Lynch (Queens Park Rangers).
Sam Gallagher (Blackburn Rovers) wins a free kick in the defensive half.
Substitution, Blackburn Rovers. Ryan Nyambe replaces Hope Akpan.
Joel Lynch (Queens Park Rangers) wins a free kick on the right wing.
Foul by Sam Gallagher (Blackburn Rovers).
Foul by James Perch (Queens Park Rangers).
Elliott Bennett (Blackburn Rovers) wins a free kick in the attacking half.
Attempt missed. Olamide Shodipo (Queens Park Rangers) header from the centre of the box is close, but misses to the left.
Foul by Pawel Wszolek (Queens Park Rangers).
Elliott Bennett (Blackburn Rovers) wins a free kick in the attacking half.
Foul by Olamide Shodipo (Queens Park Rangers).
Ben Marshall (Blackburn Rovers) wins a free kick in the defensive half.
Jake Bidwell (Queens Park Rangers) wins a free kick in the attacking half.
Foul by Liam Feeney (Blackburn Rovers).
Hand ball by Olamide Shodipo (Queens Park Rangers).
Attempt saved. Hope Akpan (Blackburn Rovers) right footed shot from outside the box is saved in the centre of the goal.
Goal!  Queens Park Rangers 1, Blackburn Rovers 2. Jake Bidwell (Queens Park Rangers) converts the penalty with a left footed shot to the high centre of the goal.
Penalty Queens Park Rangers. Yeni N'Gbakoto draws a foul in the penalty area.
Penalty conceded by Gordon Greer (Blackburn Rovers) after a foul in the penalty area.
Goal!  Queens Park Rangers 0, Blackburn Rovers 2. Liam Feeney (Blackburn Rovers) right footed shot from the centre of the box to the bottom left corner.
Attempt saved. Sam Gallagher (Blackburn Rovers) left footed shot from outside the box is saved in the top left corner.
Attempt saved. Joel Lynch (Queens Park Rangers) left footed shot from the centre of the box is saved in the centre of the goal.
Blackburn beat fellow Championship side QPR in the FA Cup third round.