Not since Bury won 3-0 at the Greenhous Meadow in March 2011 had Shrewsbury tasted defeat in front of their own supporters – with the Shakers that night managed by current Scunthorpe boss Alan Knill.
The Iron made a flying start, with Karl Hawley's fifth minute cross from the right headed in by Clarke for his second goal in as many games since arriving on loan from Charlton.
Knill's side could have been out of sight by the break as lively winger Mark Duffy, set up by Hawley, was denied by an excellent point-blank save from goalkeeper Chris Weale.
Shrewsbury found chances hard to come by. Striker Tom Bradshaw, handed his first start of the season, squandered a golden opportunity when he fired wide with only goalkeeper Sam Slocombe to beat.
The visitors continued to look the more dangerous side in the second half, with Clarke close to a second when his goalbound shot was blocked on the line by defender Darren Jones.