Ian Henderson found space down the right and slid the ball across the area for Facey to side-foot home in the fourth minute.
Bradford, on a similarly dismal run to that of Rotherham's, sought a quick response and Steven Schumacher flashed a 20-yard effort wide on ten minutes.
Rotherham failed to build on their lead and allowed Bradford to come back at them.
Marc Bridge-Wilkinson got a boot in his face on 24 minutes as he tried to head home Billy Paynter's cross but Gary Montgomery recovered.
Montgomery was forced into a top-class save on 34 minutes when he had to palm away Bridge-Wilkinson's 20-yard free-kick.
Joe Colbeck, who had been a threat down the left all afternoon, then headed Bridge Wilkinson's cross wide.
Simon Ainge was caught in possession on the edge of the area by Henderson at the start of the second half but he breathed a sigh of relief when Ricketts saved Woods' subsequent drive.
Paynter had a shot saved and flashed a 25-yard drive wide as the visitors sought to get back into the game.
They were rewarded on 54 minutes with a wonderful goal from Omar Daley, who cut in from the touchline and unleashed a fierce drive over Montgomery from 25 yards.
The momentum was with Bradford but it was Rotherham who retook the lead on 65 minutes courtesy of Ricketts' howler.
Facey put the result beyond doubt with an 18-yard drive seven minutes later that flew in off the post after Woods' initial burst had been checked.
Paynter and Eddie Johnson were both denied by goalline clearances before Woods bent a screamer around Ricketts in the 88th minute to send the home fans into raptures.