Oldham recorded their second win in five days, beating Shrewsbury thanks to Jonathan Grounds' first-half strike.
Grounds, who missed the win at Hartlepool in midweek, returned to the side to fire home after Matt Derbyshire's cross was parried.
Shrewsbury keeper Chris Weale was kept busy, saving from striker Matt Smith, while Dean Bouzanis made key stops from Matt Richards and Mark Wright.
Luke Rodgers went close to an equaliser but Jean-Yves Mvoto blocked his effort.
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Shrewsbury Town manager Graham Turner told BBC Radio Shropshire:
"It is frustrating because we had a lot of the ball during the game. We should have had a penalty too.
"The team paid the price for a slow start, yet again, and we should have come away from here with at least a point."