Goals in either half from Adam Reach and Tom Bradshaw saw Shrewsbury to a deserved first win of the season.
making his debut,
robbed Swindon defender Grant Hall on halfway and then powered forward, keeping his cool to fire past Wes Foderingham.
Swindon made little impression going forward, with a shot from Ryan Harley their best opportunity.
Substitute Bradshaw made sure of the points when he dispossessed Nathan Byrne and scored at the near post.
VIEW FROM THE DRESSING ROOM
Shrewsbury Town manager Graham Turner told BBC Radio Shropshire:
"I thought the performance deserved the win, we should have scored more goals but we worked hard and deserved the three points.
"I think what we had to do was take in mind how Swindon play - we knew what we were about - and we had a lot of opportunities and could change it on the bench, which we haven't had the option to do so far.
"The clean sheets mean a lot to the back four and the goalkeeper. We stood strong at the back - and we deserved the win.
"It hasn't been a disastrous start - we have done well so far, we've only been defeated against Bolton in the cup and Orient last week was a knock - but today makes me feel very positive."
Swindon Town caretaker manager Mark Cooper told BBC Wiltshire:
"We were thoroughly beaten, we lost too many personal battles today.
"If you don't roll your sleeves up you lose the game of football.
"We needed to show a bit of urgency, we played like a charity match. I could have still played in that today.
"We're not going to panic, we're just going to stick to what we believe in. We have to pass the ball quicker and we have to be more of a threat in the final third."
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