Debutant goalkeeper Austin, 17, made one save of note in the first half but we were largely untroubled in a game of few chances until the home side turned the screw on the hour mark.
Austin parried away first team regular Jeffrey Schlupp's effort on 27 minutes but that was it from a Foxes side also including Demarai Gray and Polish international Bartosz Kapustka until what turned out to be a match-winning purple patch in the second half.
Darnell Johnson, Gray and Harvey Barnes were all kept at bay by Austin and Kairo Mitchell had a goal ruled out for offside before the brealthrough on 74 minutes with Gray played through and making no mistake one-on-one from the left angle.