First-half goals from Jack Cork and Robbie Brady were enough to earn the Clarets a safe passage through against their near neighbours, ensuring that they retain bragging rights with a third successive win in this fixture.
Blackburn managed just the one attempt on target all evening and barely troubled their opponents in the second half, giving the 5,000 travelling supporters plenty to cheer about on the 14-mile trip back along the M65.
Burnley, now unbeaten against their arch-rivals in their last seven encounters, saw their early momentum disrupted due to an ankle injury picked up by full debutant Jonathan Walters a couple of minutes into the match.
After five minutes of treatment the Irishman was fine to continue, though he did not fully recover and Chris Wood was brought on for a debut of his own before the first half was out.
In between those two incidents Burnley largely dominated the match, but they had to wait until 21 minutes in to register their first attempt as Ashley Barnes's shot was pushed over the bar by David Raya.
The opener arrived soon after through Jack Cork, who climbed highest to head home Robbie Brady's cross for his first goal since joining from Swansea City in the summer.
Barnes then had a close-range shot kept out by a big Richie Smallwood block, before Walters's glanced header was stopped by Raya from his final involvement before being replaced.
Burnley, despite the eight changes made to their starting lineup, were beginning to make the two-division gulf between the sides count and were good value for their second goal when it arrived deep into added time.
After Wood had a shot kept out by Raya, Brady had better luck from the next attacking move as he rifled the ball into the roof of the net from a tight angle.
Wood was unable to keep his next attempt down at the end of a Charlie Taylor cross, and the £15m signing from Leeds United was also thwarted by Raya towards the end of a quiet second half.
The Blue and Whites' best hope of a route back into the game appeared to be through substitute Dominic Samuel, who had a late goal ruled out for offside to prevent a grandstand finale.
In the end those two first-half goals proved enough for Sean Dyche's men, seeing them earn a place in the hat for the third-round draw, scheduled to take place in the early hours of Thursday morning.