In a game that was lack-lustre for the most part, the points were ensured for the home side by substitute Glynn Hurst in the 73rd minute - when he pounced on some hesitant Rovers defending to earn Shrewsbury their first win in four matches and put further distance between them and the third division drop-zone.
For Rovers a second defeat in four days, however, put another dent in their play-off ambitions.
After watching his side record their eighth home win of the campaign, Town boss Gary Peters commented: "We've had a couple of games where we haven't won at home, but generally the form isn't too bad.
"You want to win games in front of your own crowd and we've managed to do that. But until we've got another couple of wins under our belts, I won't feel safe from relegation."
In a decidedly poor first half two efforts from Lewis Haldane were all Rovers had to show for their trouble - while Shrewsbury did not even manage to force a corner until the first-half injury time.
Things had to improve after the break and gradually the home side began to gain the upper-hand and, after one or two near things, Hurst finally broke the deadlock on 73 minutes, although there was a hint of good fortune about his second goal in Shrewsbury colours. The ball was hit against him by Pirates defender Craig Hinton and rolled into the net from ten yards.
His only other Shrewsbury goal was also decisive in a 1-0 home win over Wrexham shortly after he joined the club from Notts County in January.
Richard Walker had an excellent opportunity to level for Rovers shortly afterwards, but fired wide when it looked easier to score - a miss that condemned Rovers to their second 1-0 away defeat of the week.