It was the Owls' first win this season in Danny Rohl's home debut as a manager and completely deserved, former Miller Michael Smith scoring twice in a dominant first half which ought to have brought more.
A Rotherham side on the back of victory over Coventry City were bitterly disappointing so whilst Rohl was wreathed in smiles, Matt Taylor showed his anger, saying some of his players had lost a bit of his trust.
As he must with his side still bottom of the Championship, Rohl talked about how victory must be the start of something for the Owls, who lost both his first two games away from home without scoring.
"Now it's about creating a winning mindset and we have to do everything with a smile because we have to enjoy playing football,” he said.
“We have trained hard in the last 10 days and now we've seen the direction of how we want to play.
"We scored two goals and got a clean sheet and a great performance with high-intensity performance against a difficult opponent.
“The short-term goal is to stay in the league and we need a lot of points. It would be amazing to create something special because the potential here is huge.”
Smith scored both goals but as important was the performance of Anthony Musaba, whose runs behind the defence created them.
"He's very fast and good one on one," said Rohl.
"We have a weapon up front. With his pace he can attack the gaps and this is what we need from our players so we can always play on the front foot and create chances."
Taylor was scathing about his players, saying: "I'm frustrated, angry, upset in so many ways that we were so poor in so many departments, in and out of possession.
"We were second best in so many ways and in a derby you can't afford that. For 10 minutes the game was relatively balanced then we give away a breakaway goal and the whole atmosphere and scenery of what the game looked like changes.
"We just weren't bright enough in terms of getting to the ball first, winning it and using it better.
“Some of them really tried to stand up but there was not enough of an understanding.
"It's a derby, it's going to be crash, bang, wallop so get to the ball first. Sometimes you've got to put your body on the line a little bit more than we did today, sprint and just be close enough to the action to say I'm having a positive effect on the game."
Arvin Appiah was substituted to switch formation to 3-5-2 in the 26th minute of his second Championship start for Rotherham.
"I could have dragged three or four off and maybe I should have done,” said Taylor. “That is a drastic thing for a manager to do.
"You've got to trust your players but unfortunately some of them have lost a little bit of my trust in a game like that. It was exactly what we expected it to look like and too many went missing.
"I'll be looking at the video and seeing who really sprinted in all those moments because you've got to sprint in all directions.
"Sprinting and putting yourself in the action is what we've lacked."