A double from Matt Derbyshire, a tap-in for Benni McCarthy and a strike from Morten Gamst Pedersen that was simply top-class, saw Rovers ease to victory.
Luton, while showing plenty of endeavour throughout, never posed any kind of threat and in truth Blackburn could have run out winners by a much greater margin.
The result - in front of a worryingly small crowd of just 5,887 - made for an unhappy 42nd birthday for Town boss Mike Newell against his former club. It also marked Rovers' first ever win in any competition playing at Luton.
The Hatters handed a full debut to £250,000 signing Drew Talbot, who arrived at Kenilworth Road from Sheffield Wednesday on Friday in time to qualify for the game.
The 20-year-old replaced the injured Ahmet Brkovic, while the only other change to the side that beat QPR 1-0 in Tuesday's third round replay was the return of Marlon Beresford in goal after his back injury, in place of Dean Brill.
Blackburn meanwhile made three changes to the side that lost 2-1 to Watford in midweek as Ryan Nelsen, Stephen Warnock – on his Rovers debut – and Derbyshire came in for Robbie Savage, James McEveley and Shabani Nonda.
Luton started well enough and enjoyed their fair share of possession against their Premiership opponents before Rovers registered the first shot on target in the tenth minute as Beresford comfortably held Pedersen's 25-yard free-kick after Chris Coyne had flattened Warnock.
Seconds later Mark Hughes' men showed the mark of top-flight class as they took the lead in stylish fashion.
Coyne was caught out of position as Derbyshire raced on to a ball from Aaron Mokoena, and the youngster gave Beresford no chance with a thunderous angled, right-foot drive into the far corner from 20 yards.
Luton responded with an instant 25-yard effort from David Bell in the 16th minute that flew high and wide after Brad Friedel had half-punched clear a deep Sol Davis cross.
But the Hatters' afternoon took another turn for the worse just 21 minutes in as skipper Coyne, who had looked leggy in the opening exchanges, limped out of the action to be replaced by Keith Keane.
Town almost fashioned an opening in the 25th minute when Steve Robinson prodded the ball to Talbot, who had a brief glimpse of goal, but for some reason he decided to turn back inside and was tackled by Stephane Henchoz.
Luton struggled to threaten up front as Blackburn coasted until Talbot was involved again 10 minutes later as he flicked on Lewis Emanuel's corner to Richard Langley at the far post only for the ex-QPR man to be denied by David Bentley.
From the Hatters' resulting second corner, Blackburn swiftly turned defence into attack as they clinically broke to double their lead.
After claiming the cross, Friedel threw to Warnock marauding down the left and the former Liverpool man found Pedersen, who centred for Derbyshire to bravely beat Emanuel to the ball to head back across goal for McCarthy to tap home his 15th goal of the season.
Town hustled and bustled, but looked short of ideas and Rovers came through the half with embarrassing ease, Derbyshire finding the space to try another 20-yarder five minutes before the break that this time went into the arms of Beresford.
The one-way traffic continued after half-time as Warnock made another scamper forward and combined with Derbyshire in the 50th minute to tee up Brett Emerton for a curling effort over the bar from outside the penalty area.
Derbyshire almost raced through for his second in the 54th minute as he streaked on to Emerton's pass from another Rovers breakaway only for Davis to save the day for the hosts with a superbly timed tackle.
Derbyshire didn't have to wait long until he found the net again, however, as Keane fouled McCarthy on the Rovers left in the 56th minute and Pedersen switched play with a crossfield pass to Emerton, who had all the time in the world to cross from the right for Derbyshire to nod in from eight yards.
Luton brought on Dean Morgan for Bell to a chorus of boos from the home fans before the Hatters finally registered a shot on target in the 64th minute when Adam Boyd robbed Henchoz, cut inside Zurab Khizanishvili and curled a 15-yard effort at Friedel.
Rovers always looked likely to get another and Morgan denied Pedersen with a well-timed tackle in the 73rd minute as the Norwegian threatened to run clean through.
From the resulting corner though, the ball was only half-cleared and, after it found its way back to Pedersen on the left-hand corner of the penalty area, the winger found the net with a sublime 16-yard volley off the outside of his left boot that went in off the foot of the post.