Captain Chris Conn-Clarke spearheaded the Clarets’ march into the last 16 of the FA Youth Cup.
The Northern Ireland youth international earned the early penalty converted by Rhys Fenlon before curling in Burnley’s second goal himself.
And when Dylan Mooney volleyed home a third with only 20 minutes gone, Tony Philliskirk’s youngsters already had a foot in round five.
West Bromwich Albion now await the Clarets, who have made it this far for only the second time since their run to the semi-finals of the competition in 2012.
The home tie against the Baggies will be at Curzon Ashton, where Burnley launched their challenge with a 5-0 win over the National League North side.