Sheffield United had to show patience and good fitness to do it.
“I've been quite surprised actually with people's assessment of the game that we needed to do anything at half-time because I thought we were all right in the first half,” said Wilder.
“If anybody thinks we're going to have 95, 96 per cent (of possession) and dominate good players and dangerous teams, it ain't gong to happen.
“There was a little bit of sparring. I felt we had the upper hand but always had to be careful of the threats they possessed with Jack, (Anwar) El Ghazi, Wesley, (John) McGinn and players like that – really talented players for the Premier League.
“So I was all right with the first half. I didn't really say a lot other than to keep doing what we were doing, just a little bit quicker.
“We did that and got off to a fantastic start in the second half.
“People look at us as a pragmatic team with no real stars but I thought we played some great stuff, especially second half - the goals, the way we moved the ball about and restricted some really good players. Even the penalty was against the run of play.”
Like Newcastle United in the previous home game, Villa came to South Yorkshire to keep the game as tight as possible.
“The initiative is always with the home team to drive the game forward,” said Wilder. “We'll expect nothing different at Villa Park.
“Dean (Smith) wanted his team to be solid and stable after a disappointing result against Leicester.
“We had to be patient, concentrate in and our of possession because one pass they can go from box to box and we had to do the things we needed to break them down. I felt we did and I was amazed at the energy the players showed late on.
“That comes from conditioning but most importantly desire.
“The fans can't be frustrated at all, there's no need in terms of the journey this team's been on.
“It's important that from time to time they shake their head a little bit because of what we're up against. We're not going to have our own way for 95, 96 minutes.
“We've got to accept it's a sport where now and again teams won't hit the highs they want and we all have to accept that and back the group because when they do hit the heights, it's a positive feeling and a proper way of playing. “
Wilder was also impressed with the maturity of John Fleck, who scored both the goal after picking up a 17th-minute booking which will rule him out of the trip to Brighton and Hove Albion.
“It was a tough afternoon for John because he got booked again for a non-contact tackle which is disappointing for him and hurts us because he's suspended for next week,” said his manager. “He was playing against John McGinn, who he knows a lot about and is an outstanding player.
“But he produces that type of performance, unbelievably mature from John.”
David McGoldrick's first club goal since Easter continues to elude him, but the fans sang his name for the way he set up Fleck's second goal.
“He knows, I know, the supporters know, the staff know, this fellow players know how good he is,” said Wilder. “It's plain and obvious.
“He's a goal off getting up and running. You get found out if you hide in this sport and if you don't take responsibility the punters here will; be after you and they weren't. There were 29, 30,000 singing his name. They understand what he does for us.
“The positions he gets himself in are fabulous and he links play, makes us play and gives us an opportunity to get up the pitch and win matches.
“Flecky got man of the match but Didzy's performance was top class.”
Villa manager Dean Smith thought his side under-performed, but believed they were starting to frustrate the Blades before Fleck opened the scoring.
“I'm annoyed because we're better than we showed, certainly with the ball,” he said.
“I though we showed some really good defensive discipline, some good shape, and I thought they got frustrated with it but we didn't look after the ball well enough.
“We never managed the ball as well as we can with the cultured players we've got. I never felt we worked hard enough in a game of few chances. There were three chances on goal in the whole game and two of them were goals.
“I think they deserved to win because they were a little bit more enterprising in the opposition half.”