This was a deserved win for the Robins, who claimed the points with two second-half goals - the first of them a breathtaking strike from right-back Brian Wilson.
By then Rotherham had already been forced into a change with Northern Ireland international Colin Murdock limping out of the action to be replaced by Scott Wiseman.
Facey and Martin Woods of Rotherham both shot wide from distance but Cheltenham 's Steve Guinan also went close with a header from a John Finnigan cross.
Cheltenham felt they should have had a penalty when midfielder John Melligan went to ground under a challenge from Gregor Robertson but referee Danny McDermid was having none of it.
After the break Cheltenham stepped up the pressure and should have taken the lead during a crazy incident on the hour mark.
Striker Kayode Odejayi robbed defender David Worrell of possession then crashed a shot against the underside of the crossbar and out again. Guinan's follow-up shot was cleared off the line by Worrell then Odejayi shot wide from an even better position.