Blackburn booked an FA Cup sixth-round tie at home to Leicester with a hard-fought victory against Burnley.
Morten Gamst Pedersen scored the winner with five minutes remaining, thundering a fierce shot into the roof of the net.
Tugay had given Rovers the lead with a long-range effort that took a wicked deflection off midfielder Micah Hyde.
But Hyde made amends when he let rip with a dipping volley from the edge of the area to bring Burnley back in the game until Pedersen's late winner.
Robbie Savage's yellow card in the third minute suggested this would be a fiery affair between local rivals from start to finish.
But instead it was a slow-burner, only flashing into life when Hyde lit the blue-touch paper with his goal shortly before half-time.
Up until that moment, Blackburn were dominating a dour match, however, for all their possession there was no end product.
They pushed and probed but speculative pot-shots from distance were the sum of their efforts, until the 31st minute when the plan paid off, thanks to Hyde.
Savage's free-kick from the left was half-cleared and Brett Emerton's follow-up from range was deflected further from goal where Tugay unleashed a drilled right-footed shot.
It threaded through a crowd of players until glancing off Hyde and into the net beyond a flat-footed Brian Jensen who had been moving in the opposite direction.
The home goal had been coming. Burnley's response had not.
Michael Duff took a throw on the right to Hyde, a quick one-two found the Jamaican international in space and he sent an unstoppable shot looping beyond Brad Friedel.
Rovers came out with renewed vigour after the break, skipper Ryan Nelson conecting with two Pedersen corners.
His first forced a fine reflex save from Jensen while his second came back off the turf and bounced over the bar.
It seemed only a matter of time until Blackburn would regain their advantage, but they were forced to wait by Burnley's well-organised defence.
The ever-thickening shower of snow was a far cry from the sun of Dubai where Blackburn had prepared.
Their last game had been the 0-0 draw at Turf Moor, while their rivals had played two Championship matches in the intervening eight days.
After those two Nelson near-misses Burnley came back into the game, breaking on occasion to threaten the home goal.
But while they played with endeavour, it was Rovers who had the extra energy, nobody more so than Pedersen.
The Norwegian broke down the right and after his initial shot was blocked by Frank Sinclair he pounced on a loose ball ahead of Mo Camara to fire home from the angle.
Like their opener, the second had been coming and this time it proved to be the all-important winner.
Blackburn boss Mark Hughes
"Our performance wasn't what was needed, we made it hard but stuck at it without reaching the level we should.
"Credit to them, they had a game plan and stuck to it and caused us problems.
"But we're in the next round and over the two games we deserved to go through but we'll have to perform a little better if we're to progress further."
Burnley manager Steve Cotterill
"We've given them a scare and it was tough on our lads. I don't think we deserved that.
"They had the ball but it wasn't hurting us and it was a bitter blow.
"We were confident we could win the game, but it wasn't meant to be. The FA Cup's been kind to us this season but we didn't get the luck tonight."
Blackburn: Friedel, Neill, Mokoena, Nelsen, Johansson, Emerton, Savage (Flitcroft 45), Tugay, Pedersen, Dickov, Gallagher (Bothroyd 59), Bothroyd (Reid 79).
Subs Not Used: Enckelman, Short.
Goals: Tugay 31, Pedersen 86.
Burnley: Jensen, Duff, Sinclair, Cahill, Camara, Grant (Branch 83), Oster, Hyde (Roche 90), Whittingham, Valois, Moore.
Subs Not Used: Coyne, Pilkington, Scott.
Booked: Cahill, Grant.
Goals: Hyde 42.
Ref: H Webb (S Yorkshire).