With only one victory in their previous five outings and the game appearing to be slithering towards a goalless stalemate, Bournemouth's leadership challenge was losing impetus. But with five minutes left, the promotion contenders got a slice of luck.
Lee Bradbury launched a free-kick into the Shrewsbury goalmouth. Veteran substitute Steve Fletcher headed it on and Coughlan, in trying to clear, miscued his kick against the near upright and into his own goal for Bournemouth's winner.
It was a victory Bournemouth scarcely deserved. A goalless draw would have been appropriate.
A genuinely undistinguished game had few noteworthy moments, although Shrewsbury, minus injured top scorer Dave Hibbert, will look back ruefully on several moments of profligacy as the rain tumbled down. Jamie Devitt, in particular, also should have done better. On three occasions he wasted the chance to give the visitors the lead.
Bournemouth lost goalkeeper Shwan Jalal with a recurring ankle injury after an hour, but rookie replacement Dan Thomas had only one meaningful save to make before Coughlan's own goal settled an uninspiring affair.