The visitors grabbed the lead when the Tigers failed to clear a cross from the right and Lee Frecklington hooked the ball in with 15 minutes on the clock.
However, Steve Bruce’s side produced an emphatic response to lead 4-1 at the break courtesy of goals from Robert Snodgrass, Abel Hernández, Jake Livermore and Mo Diamé.
The Tigers were level when Hernàndez nodded down a Moses Odubajo cross and Snodgrass curled the ball into the top-right corner after 25 minutes.
A minute later, Rotherham failed to deal with a bouncing ball in the area and Hernández found the back of the net with an overhead kick.
The Uruguayan international fired into the side-netting as Bruce’s men threatened to run away with the game with half-time approaching, which they duly did with two more goals before the interval.
Livermore netted the third six minutes before the break as he chased an Ahmed Elmohamady pass and touched the ball past Camp before scoring from a narrow angle.
Two minutes later, Diamé made it 4-1 – beating Kirk Broadfoot to the ball before skipping past the defender and firing past Lee Camp.
The second half was always going to struggle to live up to the first but the Tigers extended their lead on the hour mark through Livermore, who fired low across goal into the far corner from 12 yards after Snodgrass had set up the chance with a clever back heel.