Midfielder David Noble was dismissed for two yellow cards before the break and Michael O'Connor was given his marching orders in the 86th minute, prompting trouble among the away fans.
Several were led away by police as bottles were thrown on the pitch in the direction of referee Eddie Ilderton.
Billy Kee was the star of the show for Burton as he pounced either side of the dismissal of Noble to set up Gary Rowett's men for a sixth successive home victory.
The visitors failed to make the most of their early pressure with Burton keeper Stuart Tomlinson well placed to make the save when the home defence allowed Mark Bradley a free header before Kee put the hosts in front.
The stocky frontman fastened onto a flick by fellow striker Michael Symes and turned Kari Arnison before shooting low past Andy Warrington in the 36th minute.
The Millers were in even deeper trouble on the stroke of half-time when Noble was given his marching orders by referee Eddie Ilderton after collecting two yellow cards in the space of four minutes for fouls on the lively Jacques Maghoma.
Kee struck again 10 minutes after the break, this time turning past Johnny Mullins on the edge of the area before finding the bottom corner.
O'Connor saw red after bringing down Maghoma in the area but the visitors were spared a heavier defeat when Symes' spot kick was saved by Warrington.