Dave Walton and Duane Darby marked their starting returns with goals to set up the win, before Darren Moss popped up with a pair from his new, more attacking berth.
Boss Gary Peters told ShrewsWeb: "I wasn't pleased with the first half as I thought we were poor and didn't deserve to go in 1-0."
Peters paid tribute to Moss as he explained his rotation system, "I played Darren Moss further forward as it was something I felt we needed to do, I've been playing too very young lads in Kelvin Langmead and Dave Edwards and
"I felt I owed it to them to take the pressure off them and rest them. Once I'd decided to do that I had to think who to put in and Darby and Walton were great choices, I knew if we got Mossey forward he gives us that extra quality."
Town travel to Bury tomorrow for the re-arranged league clash. They will be without Jamie Tolley, who is on Wales duty.
But Bury also have injury problems with five first-teamers missing. Bury boss Graham Barrow could strengthen via loan but said: "There is no point though bringing in any Tom, Dick or Harry."