An own goal from home defender Yerry Mina and a first strike for the club from substitute Lys Mousset saw the Blades extend their run without a defeat on their travels to 12 matches, with their last reverse coming in a 1-0 defeat at Swansea City on January 19.
Victory at Goodison Park saw United secure their first away win at top-flight level since triumphing at Wigan Athletic in December, 2006.
United will be aiming to avoid a third successive league defeat at Bramall Lane on Saturday when they welcome Champions League holders Liverpool, but their away statistics which have seen them pick up five points from their opening three games are stacking up rather more impressively.
Wilder said: “We have picked up a point at Bournemouth and Chelsea which are tough places to go and won at Everton, who have a fantastic home record. This result could have easily gone the other way, but last week’s result could have as well. Points are precious at any stage in the league for promoted sides and we have managed to pick up a big win.
“Our punters drive our team forward at Bramall Lane and you think promoted sides will pick up the majority of their points at home. We are bucking the trend.”
Despite the weekend triumph, it did not stop Wilder from reminding his players about the important of high standards following their club’s first success at Goodison Park since May, 1993.
While professing to being unhappy at aspects of his side’s performance, which he felt was the worst of the season in terms of ball retention, the Blades chief was happy to secure a precious victory – seven days on from his side being hugely unfortunate to lose 1-0 at home to Southampton.
Wilder said: “We had a few words and Jags (Phil Jagielka) said: ‘Gaffer, the boys have just won at Everton.’ So he put that all into perspective.
“But that is our changing room. I said that I am not expecting them to all go home disappointed – and I was expecting them to all go out and have a beer and enjoy that victory. It is a great feeling to win any game of football and they are honest boys.
“I am just a mardy a***d Yorkshire guy. We are not much fun at times!”
Saturday proved a particularly memorable occasion for two Blades players in former Everton captain Jagielka, who was given a standing ovation from home fans when he came on in the second half, and former Blues academy product John Lundstram.
The midfielder, who never played a first-team game for Everton before leaving the club, set up United’s game-clinching second goal from Mousset late on after a lovely defence-splitting pass.
Wilder said: “There was a bit of pressure with their old connections. Jags wanted to come back and do well. Lunny did and Jack (O’Connell) is a Liverpool boy as well and he wanted to do well.
“They will all be delighted, although Phil has a huge affinity to Everton.”
Former Everton international Jagielka, whose 12-year association with Everton was duly recognised by home supporters, admits that Saturday’s occasion will live long in his memory as one of the special days in his long career.
Speaking after the game, the 37-year-old said: “They are fantastic fans and we have been through thick and thin and that ovation was something I will always remember.
“Another massive day was when I came back from injury at Sporting Lisbon and when I got a great ovation. That stuck with me for a long, long time and this will be another one.
“It was my little boy’s birthday. Although I am not sure who he was supporting – I will have to find out if he was happy or sad.”