Despite falling behind to a Lionel Ainsworth strike on four minutes after being caught flat footed at the back, Rotherham pulverised the home defence for the second 45 minutes but couldn't find a breakthrough.
Shrews keeper Chris Neal was in top form, denying Nicky Law, Adam Le Fondre, Jason Taylor and Paul Warne in the final 20 minutes with a string of saves.
The Millers recovered from their early lapse which saw them fall behind and suffer a shaky 15 or 20 minutes and grew into the game just before the break before their second half assault.
Law saw two free-kicks turneed around for corners, sub Warne's 25 yarder was also tipped wide by Neal and Le Fondre failed to react to Taylor's parried shot from 20 yards as the home goal was peppered by no less than 26 efforts at goal.
Jake Robinson shot narrowly wide with a curling effort in a rare forray into the Millers half for the home side after the break.
Then in stoppage time Ryan Cresswell had the final effort for the visitors but was again denied in the six yard box.
Town held on though as they went top at the expense of Torquay and inflicted the Millers first league defeat of the season in the process.