The Hillsborough pitch had been soddened by overnight rain, but Wednesday started brightly with Sam Hutchinson heading over and Nathaniel Mendez-Laing testing Josh Vickers with a low shot after Callum Paterson and Marvin Johnson combined well to set him up.
Vickers also had to keep out a shot from Jack Hunt while Barry Bannan fired wide and Liam Palmer shot straight at the keeper towards the end of the half.
Wednesday were the better team in the first half, but the half time introduction of Ollie Rathbone gave the Millers some bite in midfield.
Freddie Ladapo struck for the visitors with a good finish after a disputed Dan Barlaser corner was met by a header from Ben Wiles just before the hour mark.
Vickers protected his side's lead, making a good save from Bannan's well-struck free-kick.
The keeper did well again to keep the hosts at bay after Mendez-Laing found himself one-on-one with him and Richard Wood blocked the follow-up.
But Michael Smith made it 2-0 with a superb curled finish from another set peice from Dan Barlasar in the 84th minute to seal the points and clear Hillsborough of pigs.