On-loan defender Ethan Ebanks-Landell scored twice, with Mark Duffy and Stefan Scougall also on target.
Wilder said: "It was entertaining and we played some really good stuff. We had to make sure we were right at it and we were.
"Big Ethan scored from set-pieces and we're satisfied. We have to play well to get into those sort of positions and to score from all over the pitch. Our opponents are in a good position in the league so I'm delighted.
"We feel we could have scored more and four were ruled out for offside, which were borderline decisions.
"Billy Sharp wants to win games of football and he's been outstanding. We're all delighted that we've won the game of football. We responded well and got after the opposition.
"We're looking for the next win. We haven't had all the results so far so we have to concentrate and move on to a tough away game on Tuesday night (at Shrewsbury)."
Port Vale first team coach Andy Smith rued his side's poor defending and failure to find the net.
"I'm very disappointed, coming from last week's results," he said.
"We came here positive and confident we could put in a good performance, but we've been done by two set plays and couldn't recover from that.
"We knew they were a good side but to give away easy goals leaves us always up against it. We plugged away and tried our best but it just wasn't to be today. They put us under a lot of pressure and we couldn't get out at times.
"We started well, but you have to take chances at this level. On another day we might have scored but today wasn't our day.
"Just before they scored, we had a great chance and you've got to take your chances at this level.
"For us it's been a good start to the season. We're very positive and happy with the work we have put in."