Second-half goals from Paul Tait and Grant Holt secured an ultimately comfortable victory for the Spotland side who are currently galloping up the League Two table.
Meanwhile, struggling Shrewsbury remain just out of the relegation zone with what appears a long fight against the drop straight back into the Conference stretching out before them.
The Gay Meadow side began brightly enough, but after a promising opening completely lost their way and managed only two efforts of note during a lacklustre second half showing that will give Peters much to ponder after only his third game in charge.
With centre-back Dave Walton beginning a three-match ban for his sending off in Shrewsbury's last game at Scunthorpe 10 days ago, Peters paired skipper Darren Tinson with Stuart Whitehead in the centre of defence and gave a debut to on-loan Preston North End striker Kelvin Langmead who twice went close in the early stages.
But the visitor's defence, well-marshalled by skipper Gareth Griffiths, withstood the Shrewsbury pressure and as the home side's early promise faded, Rochdale began to hold sway, finally making the breakthrough six minutes after the break.
When the home rearguard failed to clear their lines the ball fell to Tait who skipped past two tackles before firing confidently past Shrews keeper Scott Howie from eight yards.
Unable to make much headway going forward despite the efforts of striker Luke Rodgers, Shrewsbury found themselves with an even bigger mountain climb on 65 minutes.
Holt smashed the ball home from close range after a Greg Heald header had rebounded off the crossbar.
The game was up for Shrewsbury and despite late efforts from Martin O'Connor and substitute Duane Darby, Rochdale ran out comfortable winners.