The Millers scored an early goal and a late goal but in between barely had a chance.
They made the perfect start when Mark Burchill fed unmarked right-back Dale Tonge, who smashed home a 15-yard drive from a narrow angle after five minutes.
Macc then wasted two golden chances with Simon Yeo thumping an eight-yard drive off the crossbar in the first half and Martin Gritton glancing a six-yard header wide after the break.
Rotherham looked to have sealed the game in the 90th minute when Ian Sharps headed home.
Macc substitute Francis Green gave the home side a lifeline with a scissors kick but as James Jennings tried to collect the ball, he barged into Sharps with both seeing red from the resulting melee in the goalmouth.