Showing the confidence of a forward with eight goals in seven games, the former Plymouth striker chested down a clearance and curled an audacious 30-yard strike over the despairing dive of Mikhael Jaimez-Ruiz after 11 minutes.
The Millers continued to dominate early on with Reid curling a free-kick close after 20 minutes and Drewe Broughton testing Jaimez-Ruiz from the resulting corner.
Ian Sharps nearly gifted the home side an equaliser after 37 minutes when the towering centre-half nodded Dean Howell’s cross a yard past the upright.
The Shots showed greater urgency after the break and veteran Rotherham keeper Andy Warrington got down well to keep out Andy Sandell’s header before full-back Lewis Chalmers directed a free header of his own just wide from Scott Davies’ corner.
Warrington produced a superb double save in the closing stages to secure the points, palming out Jake Robinson’s header and then somehow stopping skipper Anthony Charles’ follow-up.