The Robins could have taken the lead inside the opening minute when Sam Deering ran on to a Marlon Pack throughball but defender Johnny Mullins did well to recover.
Rotherham's best early chance fell to Lee Frecklington but his long-range effort was pushed over the crossbar by Scott Brown.
After an even opening spell, Cheltenham took control as the half wore on with Pack shooting against the outside of a post and Paul Benson hitting an effort wide.
And the game's opener came after 32 minutes, Jermaine McGlashan unleashing a magical first-time volley which flew beyond the reach of Millers goalkeeper Andy Warrington.
There was a second for the home side four minutes before the break, Pack calmly side-footing his effort into the bottom corner from the edge of the area.
Neither side created much in the second period until the Robins netted their third after 84 minutes. Visiting keeper Warrington dropped a corner under pressure and Steve Elliott stroked the ball home from 12 yards.