Striker Billy Sharp scored two goals in the Sky Bet Championship contest, before David McGoldrick sealed the win.
United were a man down six minutes into the second half when Chris Basham was sent off after picking up a second yellow card having been adjudged to have handled Charlie Mulgrew's free-kick.
However, the numbers were evened up with 20 minutes to go when Richie Smallwood received a straight red card for a two-footed challenge on Sharp.
Wilder said: "That's right up there.
"I've got to compliment the opposition for the way they attacked the game in the first half. They freshened it up, had energy on the pitch and it was a bit of a grind for us.
"They were as good a team for 45 minutes as there's been at Bramall Lane. They were positive and we found it a bit of a struggle.
"The outcome of the game, especially when we went down to 10 men...no one would have seen the result coming."
He continued: "I thought the shape of the team was great, left two up front, played three loose in midfield,
"Dean (goalkeeper, Henderson) has made one good save but the majority of their play was in and around the areas that didn't really hurt us.
"If it has to be a grind second half we have come out the other end and we can't play our free-flowing football, we have to show our quality - and they certainly did."
The first half was a closely contested affair as both sides hit the woodwork but the Blades took advantage within two minutes of Smallwood's dismissal.
In the 73rd minute, top scorer Sharp was sent through on goal and thundered the ball into the net from close range.
Three minutes later the same player guided a volley past goalkeeper David Raya into the bottom corner and the win was sealed seven minutes from time when John Fleck set up McGoldrick, who chested in the hosts' third goal.
Rovers boss Tony Mowbray said: "It was an Intense football match, two teams who were at it. Sadly I would say the officials had the biggest impact on the game today.
"I think the referee mismanaged the game. He's come from the Premier League to the Championship, thought he'd have a nice easy day and he's guessed his way through the match with his decisions.
"He's upset the stadium, upset our bench and I think he had the biggest impact on the game.
"The last 20 minutes we need to be better. The sending off of Smallwood...I think psychologically and mentally we have to deal with that better from being in total control when it was 11 v 10 to 10 v 10 - they dealt with it better than we did.
"We were pretty good. I think when you come to Bramall Lane, if you don't stick the armour on and get the sword out, you're going to get beaten.
"They're a really good football team, with a really good manager."