Jack Cork and Robbie Brady got the goals as the Clarets eased past derby rivals Blackburn to book their place in the third round of the Carabao Cup.
Burnley have been on the wrong end of a run of cup upsets in recent seasons as their focus as often been elsewhere.
But there was no chance of a shock against League One Rovers as Sean Dyche’s side showed their Premier League pedigree to send over 5,000 travelling fans home happy along the M65.
Cork was arguably the star of the show in a peerless midfield performance which also brought him his first goal since his return to Turf Moor in the summer.
And Brady then further reinforced his place in the affection of the Clarets’ fans with a high-class second goal just before the break that all but booked Burnley’s place in the last 32 as Dyche successfully showed his squad strength.
The Clarets made eight changes to their starting line-up from Saturday's league defeat to West Bromwich Albion as they looked for a first win in the League Cup since 2013.
That meant debuts for full-backs Phil Bardsley and Charlie Taylor and a first start for former Blackburn youngster Jon Walters.
It momentarily looked like an unhappy return for Walters as he needed lengthy treatment for an ankle injury in the opening minutes before getting the all-clear to carry on.
The stoppage did little to help the flow in a frantic opening but the Clarets gradually gained a measure of control and with 21 minutes gone registered the first effort on goal.
James Tarkowski, leading by example as captain for the night, worked the ball forward for Scott Arfield to pick out Barnes, whose fierce strike from 20 yards was palmed away by goalkeeper David Raya.
With Burnley now starting to move the ball and pull the home side around, the opening goal came just four minutes later.
Again Barnes was involved with a driving run forward before laying the ball off for Brady.
Brady briefly looked up and then delivered a perfect cross for Cork to time his run perfectly and nod home his first Burnley goal since a derby winner against Preston in February, 2011 in his second loan spell as a Claret.
Unfortunately, the goal sparked unpleasant scenes as a home supporter from the Riverside Stand came onto the pitch to manhandle Tarkowski and Ashley Westwood and confront a number of Burnley players before being joined by a second invader and finally being led away.
The Clarets heeded Dyche’s call to keep their calm and took control of the tie just before the break as they took the last of a flurry of chances.
Arfield, who scored the winner here in 2015 as Burnley headed for promotion from the Championship, was the first to go close with a low shot deflected by Barnes into the body of Raya.
Walters had finally been forced to make way, with Chris Wood coming on to make his debut and the record buy from Leeds United had an immediate chance to make his mark.
Released on the break by Barnes, Wood raced into the box but with an angled drive was unable to beat the busy Raya.
But in the fourth minute of added time the Clarets’ pressure paid off with a second goal.
Brady has been a constant threat and moments after curling an effort just wide, the winger produced an explosive finish.
Accepting a neat pass from the highly impressive Cork, Brady showed a great touch to spin away Charlie Mulgrew before crashing an unstoppable shot into the roof of the net from a rapidly diminishing angle.
Rovers, who had made five changes to their starting line-up after securing a first league win of the season at Bradford City last weekend, made a double substitution at the break to try and find a way back into the contest.
But they struggled to lay a glove on the Clarets, who kept possession almost at will in the opening stages of the second half, probing for another chance which almost came their way when Taylor crossed for Wood to head wide at full stretch.
Top scorer Dominic Samuel then came off the bench for Rovers, replacing Peter Whittingham, who last played in this fixture as a loan player for the Clarets in a 2005 FA Cup tie, which Blackburn won as part of their then-domination of the derby.
The boot is now firmly on the other foot, though, as the Clarets showed the gulf in status to comfortably close out a fourth successive win over their neighbours and make it seven without defeat in the fixture under Dyche.
Rovers did have the ball in the net with 10 minutes to go after Nick Pope failed to gather a cross under pressure from his only handling error of an otherwise impressive night, but Samuel was clearly offside as he diverted home Craig Conway’s effort.
And the Clarets had two late chances to make the victory even more emphatic as Wood was denied first by Raya at his near post and then fired wide after being picked out by former Elland Road team-mate Taylor on a night Burnley did everything they had to.
Burnley: Pope, Bardsley, Tarkowski, Long, Taylor, Arfield, Cork, Westwood, Brady (Gudmundsson 78), Barnes, Walters (Wood 42). Substitutes: Heaton, Lowton, Mee, Vokes, Defour.
Booked: Bardsley, Long
Blackburn Rovers: Raya, Caddis, Ward, Mulgrew, Williams, Smallwood, Whittingham (Samuel 66), Feeney (Conway ht), Gladwin (Bennett ht), Chapman, Antonsson. Substitutes: Leutwiler, Graham, Evans, Doyle.
Referee: Simon Hooper
Attendance: 16,313 (Burnley 5,135)