It was another Clarke, Peter, who gave the visitors the perfect start as he headed home a first minute corner at the near post.
And just six minutes later Robbie Simpson glanced in Lionel Ainsworth's cross to leave Rotherham in tatters.
The Millers, who added Andy Liddell and Kevin Ellison to the starting line up, finally woke up and it was veteran L;iddell's cross on 17 minutes which set up Micky Cummins, but Clarke blocked his effort from six yards.
Ainsworth could have nicreased the visitors lead before the break, but dragged his shot wide as he cut in on the angle and saw a point blank shot pushed away by Warrington after Simpson's ball cut open the Millers back four, as Kovac also saw his goalbound effort blocked by Dale Tonge when it seemed easier to score.
Rotherham finally found a way back into the game with a deserved goal after a period of pressure on 35 minutes. Nicky Law's trickery set up Adam Le Fondre who tapped in following the wingers cut back across the area.
Ellison then had a free-kick parried by Alex Smithies in the Town goal, and after the break came closest to levelling matters as his left foot shot on the hour whistled wide.
With the Terriers closing the game out with posession football in midfield the Millers introduced Ryan Taylor and then Drewe Broughton late on, making his comeback after injury.
But it was Simpson again who could have sealed the win, this time shooting selfishly with options around him but man of the match Warrington denied him, but it mattered little as Town eased into the round two draw.