Calvin Andrew deflected Vale skipper Doug Loft's shot past diving United keeper Michael Poke in the 28th minute for what proved to be the winning goal.
The goal came against the run of play after a bright start by the home side, whose top scorer Rene Howe was denied by a top drawer Chris Neal save in the fifth minute as the Vale keeper went full stretch to tip Howe's header around a post.
Neal also flapped over Craig Easton's free kick in the first half while Poke was twice forced to save well from Andrew as United went in search of a leveller in the second half.
"We had plenty of chances and we could have stopped the goal but I have to say I thought the players were excellent in giving that sort of commitment," he said.
"I just think we need a little bit more quality and am sure we will be okay.
"I thought there were a couple of shouts for a lot of things that we didn't get but that's how it is. Before they got their goal I thought there was a foul on one of our players but the referee didn't give it and it cost us in the end.
"On the whole there were quite a few positives but we have to quickly pick up three points.
"I have said to the players that we are a good side, we have just played a side near the top of the league and did really well. We just need a little bit of fine tuning to make the game more to our advantage than the opposition's.
"We had a great start and played some good football and that's the way forward for us because we are a passing team."