A second half strike from Junior Hoilett was enough to send Rovers through to the fourth round of the FA Cup at the expense of Queens Park Rangers.
It was a game that should have been wrapped up long before it finally was, as spurned chances and good goalkeeping thwarted Steve Kean's side until the closing stages at Ewood Park.
The first half saw Rovers start brightly with Mame Biram Diouf twice going close in the opening minutes.
Then Rangers 'keeper Paddy Kenny made two superb saves, first to deny striker Diouf, then to claw a Gael Givet header aside.
Givet's match ended prematurely after a clash with Jamie Mackie, as both players were stretchered off. El-Hadji Diouf going close with an effort from the edge of the area.
Petter Vaagen Moen would go closer for the Championship league leaders with an audacious free-kick from fully 40 yards. Mark Bunn taking no chances in tipping the Norwegian's added time effort onto the crossbar.
Chances continued in the second half, Mame Biram Diouf wasteful in front of goal from Morten Gamst Pedersen's free-kick, then following a mazy run Junior Hoilett saw a shot deflected over.
Just when it looked like a replay would be required, man of the moment Junior Hoilett was on hand to ensure it would be Rovers who would progress. A neat bit of skill from El-Hadji Diouf opened up space and he found Hoilett to shift the ball and drill it low into the far corner.
Jason Roberts spurned the chance to double Rovers' lead almost immediately but couldn't connect cleanly with Josh Morris' pinpoint cross. That could have been costly when Kaspars Gorkss headed against the crossbar with six minutes to go.
But that was only a late scare as Rovers played out time with ease to book their place in Sunday's draw with a third win in four outings.
Following Rovers' impressive 3-1 win over Liverpool just the three changes were made for the FA Cup encounter.
Martin Olsson missed out with a slight calf strain sustained in Wednesday's win, Chris Samba reported flu symptoms, whilst David Dunn was rested for the cup tie.
Incoming saw a debut for 19-year-old midfielder Jason Lowe, with Grant Hanley and El-Hadji Diouf returning to the starting eleven.
Neil Warnock also made just the three changes after their Bank Holiday Monday draw with Bristol City.
Less than a minute was on the clock when Rovers fashioned their first chance, Benjani's neat flick sending Junior Hoilett racing into space to feed Mame Biram Diouf in the area, but his shot across goal went wide.
A minute later the Senegal striker was called upon again, but this time he fired straight at Rangers 'keeper Paddy Kenny.
It was a lively opening, Rovers zipping the ball around with pace, Junior Hoilett again impressing, another twisting run from the Canadian saw him drill the ball across goal but Borrowdale slid to put the ball behind as Benjani and Mame Diouf lurked in the six yard box.
Rovers continued to press and probe, a 15th minute free-kick from Morten Gamst Pedersen saw Ryan Nelsen meet the ball firmly, but unfortunately for the captain he headed well wide. A more delicate touch may well have seen the ball in the back of the net.
Two minutes later the two almost combined, but this time Nelsen couldn't flick on and Kenny made the save low down.
Then on 19 minutes the deadlock really should have been broken with two chances in the space of 20 seconds. The first saw Jason Lowe release Morten Gamst Pedersen down the right, his cross picked out Mame Biram Diouf, but Paddy Kenny flung himself acrobatically to his right to tip the ball over for a sensational save.
From the resulting corner Kenny was again the visitor's saviour, an initially cleared the ball came back out to Pedersen who picked out Gael Givet with his centre, the Frenchman's first time shot was brilliantly turned over the bar by the Rangers number one.
The visitors had been quiet up to the midway point of the half, but an impressive run and shot by the highly-rated Jamie Mackie almost saw them open the scoring, Rovers grateful for a goal-line clearance from Grant Hanley.
But on 28 minutes a 50/50 ball saw Gael Givet and Jamie Mackie collide. A stretcher was called for to help Givet leave the field of play, the home fans standing to applaud the defender. Josh Morris on to replace.
Rangers winger Jamie Mackie also needed a stretcher, Bruno Andrande on as his replacement.
When play resumed after the lengthy delay the fluency in the game suddenly deserted Ewood Park. Passes were suddenly failing to find their target as the play became scrappy. Rovers' El-Hadji Diouf firing narrowly over after Pedersen's lay-off their only subsequent chance.
As the first half entered the latter stages Neil Warnock's side grew in confidence forcing a couple of corners and enjoying a spell of possession to frustrate the home fans.
Then deep in time added on, the blue and white faithful were breathing a sigh of relief when Mark Bunn brilliantly tipped Petter Vaagan Moen's 40-yard free-kick onto the crossbar and over.
Jason Roberts returned to action at the start of the second half replacing Benjani, but in contrast to the first, the second half was slow to get going.
Rob Hulse had glanced a header wide for the visitors, then before the hour mark another Rovers chance was spurned. Morten Gamst Pedersen's floated free-kick into the area which saw Mame Biram Diouf arrive unmarked round the back, but he somehow couldn't get his shot on target as he failed to get a clean connection on the ball.
Junior Hoilett was unlucky to see his mazy run come to nothing on 64 minutes. The diminutive Canadian, again impressing, took on all-comers as he cut in from the left with the ball. But as he shaped to shoot on the edge of the area, the ball deflected just over the bar.
Then El-Hadji Diouf drilled one into the side-netting after good work from Hoilett and Roberts.
Just when it looked like being an afternoon of frustration, up popped man of the moment Junior Hoilett to finally break the deadlock on 78.
Play started down the left with El-Hadji Diouf on the run into the area, a trick creating him space, he fed Hoilett who took a touch before lashing the ball from 18 yards into the corner past the despairing dive of Paddy Kenny.
It was Hoilett's first for Rovers at Ewood Park.
It should have been 2-0 when Josh Morris put it on a plate for Roberts, but he somehow headed wide. After Hoilett's goal sixty seconds early, the Grenadian could afford a smile.
Michel Salgado made way for Amine Linganzi with eight minutes to go in a move which saw Jason Lowe move to right back. That saw a defensive line that was three quarters made up from last season's FA Youth Cup team, Ryan Nelsen the only senior alongside Hanley, Morris and Lowe.
The visitors certainly weren't down and out and were only the thickness of the crossbar away from drawing level with six minutes to go when a Petter Vaagan Moen free-kick was headed against the bar by Kaspars Gorkss.
As with the first half four additional were shown, but Rovers played them out deep in the visitor's half to ensure that it was their name associated with ball number 15 in Sunday afternoon's fourth round draw.
ROVERS: Bunn, Salgado (sub Linganzi 82 mins), Hanley, Nelsen (c), Givet (sub Morris 30 mins), Hoilett, Lowe, Pedersen, EH Diouf, Benjani (sub Roberts 46 mins), MB Diouf.
Subs not used: Fielding (GK), Goulon, Cotton.
QPR: Kenny, Orr, Hill, Derry (c), Clarke, Faurlin (sub Cook 81 mins), Mackie (sub Andrade 32 mins), Gorkss, Hulse (sub Doughty 88 mins), Vaagan Moen, Borrowdale.
Subs not used: Cerny (GK), Tofas, Harryman.
Booked: Borrowdale, Derry (QPR).