The Millers tore into Shrewsbury from the first whistle and raced into a ninth-minute lead when the lively Kieran Agard's cross from the right was powerfully headed home by Tom Hitchcock.
Tom Eaves quickly struck the inside of a post at the other end as Shrewsbury briefly threatened to equalise before Rotherham doubled their advantage in the 17th minute when Ben Pringle fired high into the net from the edge of the penalty area.
Shrews goalkeeper Chris Weale had already made a brilliant save to claw away Mark Bradley's header, but he was left badly exposed again when Rotherham right-back James Tavernier, who started the season on loan at the Greenhous Meadow, exchanged passes with Hitchcock to neatly make it 3-0.
Pringle then struck the crossbar with a 20-yard free kick on the stroke of half-time as Rotherham continued to look dangerous.
Shrewsbury were better in the second period, but rarely threatened and have now failed to score in their last five home matches - a miserable sequence for Graham Turner's side, who sit just above the relegation zone.