The Fifers took the lead with half an hour played when Nikolay Todorov slipped the ball through the legs of Celtic goalkeeper Ross Doolan.
Celtic drew level six minutes into the second half when Jack Aitchison shot home. Crossan hit the winner when he tucked the ball into the net after Cowden keeper David McGurn could only push away a Calvin Miller shot.
With quarter of an hour to go the Cowdenbeath’s Chris Turner was dismissed after he had been substituted for apparently making gestures to the travelling support. His replacement, Gary Glen, was not allowed to come on.
Forfar got the better of Aberdeen’s under-20 side with a 3-1 success at North Lodge Park. Dons youngster Sam Roscoe was shown a straight red card after 19 minutes and Josh Peters edged the Angus side ahead on 33 minutes.
Allan Smith doubled Forfar’s lead on 54 minutes and Peters netted again after Kesi Omokolun had pulled a goal back for the Dons.
Hearts colts also exited the competition as they went down 2-0 to Elgin at Borough Briggs.
Shane Sutherland accepted a knock down before turning the ball in to give the hosts the lead 12 minutes from the break with Kyle Macleod grabbing the second goal early in the second half.
Queen’s Park’s Gregor Fotheringham hit the decisive penalty in a 6-5 shoot-out success over Partick Thistle’s young Jags at Firhill following a 1-1 draw.
Thistle took the lead three minutes into the second half through Michael McMullin but the Spiders levelled two minutes from time when John Carter scored, with the Firhill side then reduced to ten men in extra time when David Syme was dismissed.
Albion Rovers ended Hamilton’s under-20 side’s involvement with a 2-0 victory in Coatbridge, Ross Dunlop and Mark Ferry scoring.
Airdrie also won a Lanarkshire derby as they defeated Motherwell under-20 2-1 at Fir Park with Iain Russell and Andy Ryan scoring. Dylan Mackin netted for the Steelmen.
Cove Rangers stunned hosts Brechin City after only 90 seconds through Harry Milne however the Glebe Park men hit back to win 4-1, Finn Graham, Andy Jackson (two) and Ross Caldwell scoring.
Peterhead roared back from two goals down to defeat Brora Rangers 3-2 thanks to goals in the last 16 minutes from Jordan Brown, Rory McAllister and Leighton McIntosh.
Zander Sutherland shot the Highland League side into the lead on 18 minutes and a long kick out from goalkeeper Joe Malin led to Brora’s second on 48 minutes from Paul Brindle but Peterhead prevailed.
Stranraer cruised past Spartans 7-1 at home with Craig Malcolm helping himself to four goals.
Mark McGuigan, Willie Gibson and Kyle Turner also scored for the Stair Park side, with Eddie Malone netting Spartans’ consolation.