The Millers were undone by former striker Tom Pope who scored against his old club for the fifth time this season.
Pope added a second eight minutes after Louis Dodds opened the scoring for Vale.
Kieran Agard gave Rotherham hope eight minutes from the end, but Rotherham could not add to that as Vale held out against tremendous home pressure.
"We were disappointed that the game was called off at the weekend," Adams said. "And I've had them round the track over Christmas to prepare for today and we do it because we are professional and it has paid dividends today and that's why we do it.
"As a result we've come away with three points. Coming into this stadium inspired me because it's a magnificent new stadium, a full house and against a team that were flying high - and I still maintain Rotherham will be there or there abouts come the end of the season - so we needed some big performances and we got them.
"But in the end its only three points. We are half way through the season and we have 43 points. If we replicate that through the rest of the season we will achieve all our goals and ambitions.
"Our results so far speak for themselves. We are up there to be shot at. We have just got to concentrate on ourselves and prepare for games and the effort and enthusiasm they have shown today will carry them a long way."