A whirlwind second half display from Rovers saw them comfortably book themselves a place in the fifth round of the FA Cup with Budweiser.
After a scrappy first half that was memorable only for Colin Kazim-Richard's 44th minute opener, Rovers lit up Pride Park with a scintillating second 45.
Chances came and went before Rovers defender Scott Dann hit a stunning second goal for the visitors, emphatically lashing home from Danny Murphy's pass.
A 17th Rovers goal for striker Jordan Rhodes soon followed as the visiting side made it through to the next round with ease.
Michael Appleton made just the one change from the side that drew with Brighton & Hove Albion in midweek.
With Todd Kane cup-tied it meant a reshuffle for the Rovers boss with Jason Lowe moving to right back, Morten Gamst Pedersen into the centre of midfield and Joshua King coming into the side after injury to occupy the right wing spot.
After a slow start to proceedings it was Rovers who were the first to threaten. It came from a 7th minute free-kick, but as Morten Gamst Pedersen whipped the ball into the back post, Scott Dann charged in to get a touch but the ball ran agonisingly wide of goal.
A minute later and Rovers were dealt a blow as Josh King pulled up with what looked like a reoccurrence of his hamstring injury. The Norwegian had only just returned to training so to lose him so quickly was harsh. Ruben Rochina came on to replace.
After that the game was by and large a scrappy affair with little flow from either side. A bullet free-kick from Morten Gamst Pedersen almost catching out Adam Legzdins in the Rams goal.
Then a lovely ball from Danny Murphy set Jason Lowe away down the right, his centre was aimed for Jordan Rhodes but the striker couldn't make the most of the chance.
As the half wore on the home side came more into the game with the great advantage territorially. A good run from Jeff Hendricks saw the midfielder find Conor Sammon in the area but his turn and shot was well off target.
On 44 the deadlock was finally broken and it was first blood to the Lancashire side. A Derby attack was cleared away by Jason Lowe and as Jordan Rhodes let the ball run through Colin Kazim-Richards took advantage of some hesitant defending by Rams captain Richard Keogh to burst through on goal to fire past Legzdins for his fourth goal of the campaign.
As added time at the end of the first half drew to a close Derby threatened a quick reaction as Sammon fed John Brayford but Jake Kean was down well to claim.
Neither side made any further changes at the start of the second as Rovers started the stronger of the two side.
An error from Jake Kean almost handed the home side a way back into the game when his clearance was blocked by Conor Sammon but the young stopper redeemed himself to claim Jamie Ward's centre.
Rovers countered with lovely spell of passing play, it ended with Scott Dann feeding Ruben Rochina but the Spaniard fired just wide.
Two chances followed for Rovers that left you just wondering if they would regret not taking them, firstly Jordan Rhodes was flagged offside as he crossed to where Markus Olsson arrived to find the back of the net. Then another great chance went begging as Ruben Rochina was denied by Adam Legzdins in the Derby goal.
However from the resulting corner kick weren't to be denied a further time. Pedersen's inswinger was cleared initially but as Danny Murphy lofted the ball into the area Scott Dann hit a sumptuous strike that flew into the top corner of the goal.
Five minutes later and the tie was over as Rovers netted a 71st minute third. Rochina and Murphy combining before Markus Olsson scampered forward, he looked to be crowded out in the area but Jordan Rhodes wasn't and the striker added to his season's goal tally by floating the ball into the back of the net with aplomb.
With the game won Rovers went in search of further goals, substitute David Dunn combining well with Danny Murphy before Rochina saw a shot tipped round the post.
Then with four minutes remaining a scramble from a Pedersen corner saw the ball fall to Rhodes but under pressure he scooped the ball over the bar.
Four additional minutes were shown, but unlike Tuesday night there was to be no late drama as Rovers saw out time with ease, They can now look forward to the 5th round draw on Sunday evening.
DERBY COUNTY: Legzdins, Brayford, Roberts, Bryson, Keogh (c), Coutts, Hendrick, Ward (sub Jacobs 72 mins), O'Brien (sub O'Connor 83 mins), Hughes (sub Davies 75 mins), Sammon.
Subs not used: Fielding (GK), Doyle, Freeman, Bennett.
ROVERS: Kean, Lowe, Dann, Hanley, Martin Olsson, King (sub Rochina 10 mins), Murphy (c), Pedersen, Markus Olsson (sub Dunn 83 mins), Kazim-Richards, Rhodes.
Subs not used: Usai (GK), Givet, Fabio Nunes, Nuno Gomes, Goodwillie.
Goals: Kazim-Richards 44 mins, Dann 66 mins, Rhodes 71 mins.
Booked: Hanley, Markus Olsson, Rochina.