An early goal from Dan Agyei was enough to take the Clarets into the last 16 of the Premier League Cup as they completed their great escape from the group stage.
An opening 7-1 defeat at Bournemouth made it look a long way to the knock-out rounds.
But a brilliant unbeaten run since saw Steve Stone’s side top the group to set up a home tie next.
Going into their final game, the Clarets were sitting in bottom spot and knew nothing less than victory would do them.
That was the same scenario facing West Brom as Liverpool waited in the wings to sneak through with Bournemouth in the event of a draw.