Maximum points were secured by James Constable’s 16th-minute tap-in, only the side’s third goal in six games.
A failure to take chances has been United’s Achilles’ heel during a five-game winless run and again they spurned clear-cut opportunities.
But a single goal was enough to claim a deserved victory, which thrilled Wilder.
He said: “Every win is important, but that was a big three points for us.
“We always felt we were one performance and one result away from going again and we’ve got to make sure we do that.
“Over the last two or three weeks the performances have been OK against some decent sides and we were up against another one.
“I thought we dominated the game, although I would have liked to have scored another couple of goals because I think our play deserved that.
“We looked bright and on the front foot. It was an uncomfortable last 20-25 minutes because we knew the gap should have been bigger than it was.
“You always put pressure on yourself to win, but when you’ve not done that for a few games you have to go looking for it.
“We were bold in our selection again, we were bold in our approach and we got our reward.
“Nothing has changed in the overall process between winning the four games over Christmas and the last few.
“You keep believing.”
United had to make yet another late enforced change to the side, as Alfie Potter succumbed to an illness on Friday night.
Tony Capaldi did not travel due to a similar virus, which meant the visitors could only name six substitutes.
Wilder is optimistic the winger will recover in time for Saturday’s game at home to York City, but praised his replacement Josh Parker, who was already being considered for selection after encouraging performances as a substitute.
“Hopefully Alfie will be available for the next game,” the United boss said.
“In the middle of the night he got taken ill and I got the dreaded (physio) Andy Lord phone call in the morning.
“But we dealt with it and I was delighted with Josh Parker, who I thought was excellent.
“He deserved his chance and he was in our mind to play him in the game anyway.”