Carlos Carvalhal said the Owls deserved the late, late reward that sent his side back into the top six.
A dogged and determined Rotherham were finally undone in stoppage time when Steven Fletcher decided a dour South Yorkshire derby from the penalty spot.
And Carvalhal said: “We were very patient today and we deserved the victory.
“We changed the way we played, we pushed more men forward, and when this happens you normally get rewards.
“With Rotherham, we have not beaten them at home for a long time, they do well here and that can get into players’ minds.
“They played strong and compact, they are fighting for their lives, so we broke down the walls in many ways today.”
The head coach issued an injury update as the Owls head into a nine-day period without a game before heading to table-toppers Newcastle on Boxing Day.
He said: “Almen Abdi had to come off with a shoulder injury so we will see how he is.
“Kieran Lee had a problem so we decided to keep him off the pitch for the second half.
“Barry Bannan has been playing with some pain so he was not in the squad today.
“So we have players coming back to help make us stronger – Fernando Forestieri, Gary Hooper, Jack Hunt, Will Buckley, Almen, Barry, Kieran….we will get continue to get better.”