Second-half goals from Dylan Moonan and Corey Brennan sent the Clarets into the quarter-finals of the FA Youth Cup as they wound back the clock in superb style at the Tameside Stadium.
Burnley beat West Brom en route to the semi-finals of the competition in 2012, when they also knocked out Fulham.
And it’s Fulham or Manchester City who now await Tony Philliskirk’s men in the last eight, with the pair playing early next month for the right to host a Burnley team who are yet to concede a goal in their best run for eight years.
Curzon Ashton and Mansfield Town were brushed aside in rounds three and four as the Clarets made their favourite’s tag count.
But this time the boot was on the other foot with Albion, who had previously knocked out Scunthorpe United and Middlesbrough, the fancied side given their higher ranking as a Premier League Under-18 side.
The Clarets are currently operating at a level below but thoroughly deserved their victory with an excellent performance capped by two goals inside the last 12 minutes in front of watching first-team manager Sean Dyche and his first-team staff and an appreciative which celebrated with the players at the end.
Burnley had as good as won their opening two ties with three-goal bursts inside the first 20 minutes.
But this was always going to be a more competitive affair with little between the sides in an entertaining first half.
Baggies midfielder Toby King skimmed the crossbar with a long-range effort and Clarets keeper Harry Allen twice had to save from Alex Gilbert with his legs.
But Burnley also had chances of their own as they impressively closed the gap in status between the two teams.
As they had in the previous rounds, widemen Chris Conn-Clarke and Rhys Fenlon caused problems and the front pair of Joe McGlynn and Max Thompson – starting his first game of the run – gave the Baggies’ back line a tough test.
McGlynn’s lay-off for Thompson brought the Clarets their best chance before the break but the former Everton striker couldn’t beat Josh Griffiths.
The Baggies’ keeper also gathered an effort from Conn-Clarke, who saw another effort blocked, while Ben Woods also fired just wide in a bright start from the home side.
It was just as tight after the break as both sides battled for the breakthrough.
Clarets’ full-back Matty Rain thought he had provided it following a superb run and link-up with the impressive McGlynn but needing a second attempt to force the ball home and did so from an off-side position.
The visitors then had a spell of pressure with Jacob Wakeling twice going close, first forcing Allen to save at his near post and then grazing the far upright with a deflected effort.
But with 12 minutes to go the Clarets grabbed the opening goal to put one foot in the last eight.
Conn-Clarke delivered a corner from the left and midfielder Moonan, as he had done at Mansfield, was in the right place to stick out a boot and cleverly flick the ball inside the far post.
Rather than sit on their lead, the Clarets then went for the kill.
McGlynn was denied the goal his performance deserved when he was denied by Griffiths after being released by Woods.
But any prospect of a Baggies fightback was killed off a minute from time when substitute Brennan struck.
This time the pacy Fenlon, who enjoyed an outstanding night, sprung the Albion defence but saw his effort hit a post.
Undeterred, he kept his composure to retrieve the loss ball and tee up Brennan.
And with virtually his first touch, the midfielder drilled the ball into the roof of the net to seal the Clarets’ passage through on a famous night for Philliskirk’s young charges.
Burnley: Allen; Patterson, Rooney, Pruti, Rain; Fenlon, Moonan, Woods, Conn-Clarke (Brennan 86); Thompson (George 73), McGlynn (Mellon 90). Substitutes: Waller, Chima, Connolly, Armstrong.
West Bromwich Albion: Griffiths; Ingram, Taylor, Williams, Delaney; Fellows (Gardner-Hickman HT), King (Richards 83), Andrews, Gilbert; Wakeling, Thorndike (Faal 86). Substitutes: Gardner-Hickman, Emery, Ashworth, Teixera, Iroegbunam.
Referee: Aaron Bannister