But they had to rely on an own goal from Rotherham defender Ian Sharps after Ryan Taylor had cancelled out Nick Chadwick's opener.
Grant Holt and Chadwick were the main culprits as the visitors bossed the first half but they blew a string of chances.
Rotherham saw an earlier chance cleared after Ryan Taylor's cross into the box had the visitors in trouble after three minutes but then the Yorkshire outfit were forced to be spectators as Shrewsbury set the pace.
Paul Simpson's side created a string of first-half chances but they failed to cash in as Rotherham defended desperately.
After five minutes a right-wing cross from Chris Humphrey found top-scorer Grant Holt but he failed to add to his tally of 27 goals when he headed straight at keeper Andy Warrington.
Holt and strike partner Nick Chadwick were the chief culprits as the visitors continued to squander chance after chance.
Even skipper Graham Coughlan - the former Rotherham defender - got in on the act heading wide from a Steve Leslie cross.
Another Leslie cross was then headed over by Holt and a clever shot on the turn from the same player flew over the bar.
Chadwick then hit the post from point-blank range and Leslie was unable to turn the rebound home, and when Holt chipped a neat ball to the unmarked Chadwick, his header was off-target.
A minute before the break Neil Ashton found Holt before Paul Murray's short ball fed Chadwick who forced his way into the area and drilled a low shot past Warrington.
Rotherham levelled after 70 minutes with their first attempt on goal when Ryan Taylor clipped in a low shot after Ian Sharps had headed the ball down.
Six minutes later Sharps attempted to clear Ashton's low cross into the box and sliced the ball past his own keeper and Shrewsbury held on to claim a valuable three points.