The Millers continued their unbeaten start to the season after a superb second-half showing where goals from Kieran Agard, Daniel Nardiello and Rob Milsom overturned a first-half deficit and blew the Blades away.
It was their first league victory over their neighbours since 1981 and became a Sheffield double after Evans' men knocked United's city rivals Wednesday out of the Capital One Cup earlier this season.
"In the second half we took the shackles off the players and they delivered," Evans said.
"At 3-1 Sheffield United probably got off lightly because if we had taken advantage of the opportunities we created on the break we could have beaten them by more, but it was a comfortable win.
"This football club should not have waited as long as it has to beat the two Sheffield clubs, they are not Premier League clubs anymore."
The Millers' fightback, which came after Evans changed his tactics at half-time after Jose Baxter's first-half goal had given the Blades the lead, was kick-started by Agard's thumping 25-yard effort, which earned full praise from the Millers boss.
"Kieran Agard is a player with a heart the size of a lion," Evans added. "He has no hesitation in taking a shot on and that is bravery.
"When he hit that everyone was expecting him to pass it, but it was a fantastic strike and not many keepers will save that."
- Sports & Recreation
- Kieran Agard
- Sheffield United