Rovers bowed out of the Carabao Cup at the second round stage as Burnley claimed a 2-0 victory at Ewood Park.
The £23m pairing of Jack Cork and Robbie Brady did the damage, with both players grabbing a goal and an assist in the first half.
Tony Mowbray's side started brightly, but found themselves behind on 27 minutes when Cork headed home Brady's right-wing cross.
The same duo combined to double Burnley's lead in first-half stoppage time, as Cork picked out Brady in the box and the Irishman rifled the ball into the roof of the net.
Rovers plugged away in seach of a way back into the game after the break, with substitute Dominic Samuel seeing a goal ruled out for offside, but a relatively uneventful second half passed without incident, as Burnley progressed to round three.
Ahead of the game, Rovers made five changes to the side that beat Bradford at the weekend, with summer signings Ben Gladwin, Harry Chapman and Marcus Antonsson all handed their first starts.
Peter Whittingham, who once had a loan spell with Burnley, and Liam Feeney also came into the starting line-up.
Samuel, Corry Evans, Elliott Bennett and Craig Conway dropped to the bench, whilst Bradley Dack missed out with the thigh strain he picked up in the victory at the Northern Commercials Stadium.
Burnley made eight changes to the side that lost at home to West Brom at the weekend, with new £15m signing Chris Wood named amongst the substitutes.
Rovers more than matched their Premier League visitors in the early exchanges and created the game's first chance on 14 minutes.
Feeney's free-kick was cleared only as far as Whittingham and his first-time volley deflected just wide.
Burnley's first effort at goal came at the midway point in the half. Scott Arfield played the ball into the feet of Ashley Barnes, whose crisp left-foot strike was headed for the top corner, but David Raya made a smart save.
With the visitors starting to gain a grip on the game, they opened the scoring on 27 minutes.
Brady swung in a cross from the right and Cork rose highest in the middle to head home.
Burnley threatened again on 35 minutes. A free-kick into the area caused concern in the Rovers defence and Barnes' shot deflected off Richie Smallwood and looped over the bar.
Former Rovers youngster Jonathan Walters headed an effort straight at Raya on 42 minutes and that would prove to be his last involvement as he then limped off to be replaced by Wood.
The change sparked a flurry of chances as the half drew to a close.
Raya was called upon to make a superb double save, as Arfield's cross-shot was deflected goalwards by Barnes, but the Rovers keeper showed razor-sharp reactions to keep it out, before being alert to palm away the rebound as Wood looked to pounce.
As six minutes of added time went up on the board, Brady fired a long-range effort just wide, before Barnes played in Wood, one-on-one with Raya, who made another superb save diving away to his left.
But in the fourth minute of added time, Burnley's pressure eventually told. Cork centred from the left into the feet of Brady, who advanced towards the byline, before rifling the ball into the roof of the net from an acute angle.
The half ended with Charlie Mulgrew curling a trademark free-kick onto the roof of the Burnley net.
Rovers made a double change at the break, with Conway and Bennett replacing Gladwin and Feeney, but the action on the pitch failed to match the intensity from the stands.
Brady fired a free-kick straight at Raya and Wood headed over the bar, as both sides struggled to create chances.
Mowbray made his final throw of the dice on 66 minutes, with Samuel brought on to replace Whittingham, and the substitute was inches away from pulling a goal back 10 minutes later.
Mulgrew whipped in a wicked free-kick from the right touchline and Samuel just couldn't stretch far enough to connect at the back post.
Samuel had the ball in the back of the Burnley net on 81 minutes, but it was ruled out for offside. Paul Caddis crossed from the right, goalkeeper Nick Pope dropped his catch and as Conway prodded the ball forward, Samuel diverted it in, but from an offside position.
In the closing stages, Wood blazed over the bar at one end and Bennett dragged a shot just wide, as Burnley secured the East Lancashire spoils.
Rovers are back in action at Ewood Park on Saturday, with MK Dons the visitors for the fourth League One fixture of the season.
ROVERS: Raya, Caddis, Ward, Mulgrew, Williams, Feeney (Bennett 46), Smallwood, Whittingham (Samuel 66), Chapman, Gladwin (Conway 46), Antonsson.
Subs not used: Leutwiler, Doyle, Evans, Graham.
BURNLEY: Pope, Taylor, Coek, Tarkowski, Barnes, Brady (Gudmundsson 78), Westwood, Walters (Wood 43), Bardsley, Long, Arfield.
Subs not used: Heaton, Lowton, Mee, Vokes, Defour.
Goals: Cork (27), Brady (45+4)
Booked: Bardsley, Long
Attendance: 16,313 (5,135)