Kieran Agard grabbed his 18th goal of the season by earning and converting a penalty in first-half stoppage to ensure Evans' men triumphed at a blustery London Road.
The one-time Posh loanee was bundled over by Ben Nugent, a centre-back currently on loan at Posh from Cardiff, following a slick move down the Rotherham right.
The visitors, who have not lost since New Year's Day, were denied a second goal on the hour by a fine save as Bobby Olejnik thwarted MIllers man Nicky Adams in a one-on-one situation following a delightful pass from Ben Pringle.
Rotherham keeper Adam Collin also produced two super saves as his team boosted the best away record in League One.
He kept out Nicky Ajose's glorious opportunity in the opening period and then dashed from line to deny Conor Washington at point-blank range midway through the second half.