The Black Cats ace snapped up two in ten first-half minutes as Rotherham's stubborn resistance faltered.
It put the game beyond Ronnie Moore's Yorkshire outfit and sent them crashing to their first defeat in nine games.
The victory, on top of Sunderland's 3-0 Boxing Day win over Bradford, puts Mick McCarthy's men back on track for a Premiership return.
Stewart struck in typical fashion in the 29th minute, plundering his eight of the season with a diving header from close range after Mike Pollitt's brilliant reaction save to parry Joachim Bjorklund's header.
And when stand-in centre-back Guy Branston challenged Tommy Smith in the area ten minutes later, referee Chris Foy handed Sunderland a penalty and Stewart crashed in the spot-kick.
Rotherham were feeling hard done by after the ref ignored a tug in the area on Paul Warne and let off Jason McAteer with a yellow card after a brutal challenge that saw defender Shaun Barker stretchered off.
The Millers were always second best and might have suffered more after Darren Byfield's showboating gave the ball away to Smith, but Pollitt saved well.
And Pollitt had to be alert to save at Stewart's feet when he linked brilliantly with McAteer.
A 30-yarder from Jeff Whitley ran wide after Branston headed out a dangerous ball and after Julio Arca robbed Byfield, Pollitt held on to his long-range effort.
But Rotherham held out stylish Sunderland after the break and Byfield squeezed his shot wide in the home side's best effort.
Even wonderkid Will Hoskins, the 17-year-old whose double killed off Wigan on Boxing Day, couldn't turn on the magic when he came off the bench.