A second minute lob from greig Spence calmed any nerves with the former Alloa striker doubling the lead 20 minutes later.
An opportunist strike from Tony Watt shortly afterwards put the issue beyond doubt.
CELTIC: Feely; O’Donnell, Toshney, Jones, Brennan; Irvine, McGregor, Bagshaw, F Twardzik: Spence, Watt
SUBS: Thomson, Fraser, Lowdon, Atajic, Gormley, P Twardzik