The visitors looked vulnerable from set-plays, though, and four consecutive corners eventually resulted in Kelvin Langmead heading in from Craig Disley's cross.
The same player was again the provider in the 24th minute as his free-kick was nodded home by Shane Cansdell-Sherriff.
Hereford improved after the break and dominated the first 20 minutes of the second half but Shrewsbury went closest with a Jake Robinson header against the crossbar.
The home side put the result beyond doubt in the 79th minute when Coughlan grabbed the third goal from another corner.
Source: Team Talk
Source: Team Talk