Kevin Miller missed from six yards for Wolves early on before Martin McIntosh headed home Chris Sedgwick's cross to give rock-bottom Rotherham the lead.
Colin Cameron and Miller both went close from long range before Cooper advanced from 35 yards before equalising with a swerving strike.
And with 11 minutes left Korean Ki-Hyeon Seol picked out Cort, who steered the winner past Mike Pollitt.
Rotherham boss Ronnie Moore:
"At the end of the day our second-half performance was not good enough.
"Their first goal changed the game it was big, big moment and a keeper of
Mike Pollitt's class shouldn't be beaten from that range.
"Their second goal was down to dozy defending and we have another defeat out of a game we looked like winning.
"The problem now is we do not know how to win and we do not know how to hold
Wolves caretaker boss Stuart Gray:
"In the first half our final ball let us down and their goal knocked us sideways. But we dominated after the break and we worked hard for each other.
"Ki-Hyeon Seol did very well after he came on and Kevin Cooper caused Rotherham
problems down both flanks with his goal giving us a big lift.
"I have not been interviewed for the job and I am not on the shortlist. The only way I am going to get the job is if we keep winning games."
Rotherham: Pollitt, Stockdale, Shaun Barker, McIntosh, Hurst,
Sedgwick, Mullin, McLaren, Proctor, Butler (Monkhouse 74), Junior.
Subs Not Used: Montgomery, Richard Barker, Gilchrist, Scott.
Goals: McIntosh 36.
Wolverhampton: Oakes, Lowe, Bischoff (Craddock 90), Lescott, Naylor, Newton (Seol 54), Cameron, Olofinjana, Cooper, Cort, Miller (Clarke 84).
Subs Not Used: Murray, Andrews.
Goals: Cooper 69, Cort 79.
Ref: M Halsey (Lancashire).