Two goals from Marc Richards, one being helped into the net by keeper Ian Bennett, was enough to win the game for Vale and although Utd did get back into the game with a goal from Billy Sharp, Adams registered his first win in his second game in charge.
"There will be a few tears in my family after this result, but I am new to the football club and it is important that I stamp my mark on it and results like this will only help me," Adams said after the game.
"We are not the most eye-catching side, but I don't think that could be labelled at us in this game. I thought we tried to play as best we could when we could and defended well, we had a bit if luck with 'Benno' but we will take it."
Vale goalkeeper Chris Martin also came in for some praise from the manager: "Before I got to the club they said he had done well at the end of last season, but you are always wary of an 18-year-old kid. He has done fantastically well, he has showed what a great prospect he is going to be."