Lewis Richardson led the charge as the Clarets eased into round four of the FA Youth Cup.
Richardson – making a rare appearance in the Under-18s – was too hot to handle as Tony Philliskirk’s side booked a trip to Mansfield Town in the last 32 of the competition.
The England Youth international was tripped to earn an early penalty which was converted by Rhys Fenlon before slotting home the second himself.
And he then claimed the final touch to a Chris Conn-Clarke as the Clarets rattled in three second-half goals to complete their biggest win of the season.
The youths have suffered their share of shock exits in recent seasons and might have expected a tricky test against a Curzon side that had already knocked out Blackpool and Oldham Athletic as part of a superb six-game winning run to get this far.
But in truth, another upset was never on the cards as the Clarets illustrated the gulf in status with a measured performance that could have yielded more goals.
Any potential nerves were settled with just over a quarter of an hour gone when Richardson was too quick for Blerti Jacaj and was upended in the box by the Curzon defender.
Winger Fenlon took responsibility to fire the Clarets in front and the lead was never threatened.
Richardson and strike partner Joe McGlynn – no strangers to the Tameside Stadium from their appearances here for the Clarets’ Under-23s – had too much for the non-leaguers.
And when they broke clear again, it was McGlynn’s low cross that Richardson coolly tucked away with a left-foot finish 10 minutes before the break.
Any prospect of a chance at the other end was invariably snuffed out by the impressive Jake Rooney in tandem with Edon Pruti.
And 12 minutes into the second half the Clarets took complete control with their third goal.
Again, McGlynn did well to keep the ball alive and pick out captain Conn-Clarke, whose in-swinging cross found the far corner with Richardson claiming the slightest of touches.
Richardson should have guaranteed getting his name on the scoresheet for at least a second time with a couple more chances the 16-year-old failed to convert.
But with the job done he and McGlynn, who went close to the goal he deserved with a curling shot just over the bar, were replaced as the Clarets added the late goals to reflect their superiority.
The dangerous Conn-Clarke had again gone close when new recruit Max Thompson, making his first appearance since completing his signing from Everton, teed up fellow substitute Mitch George for a clinical side-foot finish.
And hard-working midfielder Ben Woods then got in on the act eight minutes from the end when he picked out the bottom corner from 15 yards to complete an efficient night’s work and set up a trip to Field Mill some time next month.
Curzon Ashton: Lovell; Gemmell, Jacaj, McCann, Dolan (Dawson 57); Grewal, O’Mara, Ehigator, Sloan; Bertenshaw (Owen 63), Mulvey (Lord 63). Substitutes: Edmondson, Hanley-Watts.
Burnley: Thomas; Patterson, Rooney, Pruti, Rain; Fenlon, Moonan (Armstrong 80), Woods, Conn-Clarke; Richardson (Thompson 73), McGlynn (George 73). Substitutes: Waller, Chima.
Referee: Zharir Mustafa