Calvin Andrew deflected 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.
Adams said: "We lost a game last week and we had a magnificent response today from a group of players who rolled their sleeves up and ground out a 1-0 win away from home. I can't ask any more of them.
"Torquay also gave it a good go today. I was disappointed to see Alan Knill appointed (as interim manager at Torquay) earlier in the week because I thought that would give them a boost. He is a good manager and he knows the league.
"There were two teams that wanted to attack today and Torquay to a man can be proud of their efforts.
"The character we showed today was absolutely tremendous. In terms of effort and commitment it was all there.
"We have answered a few critics today, we are a close-knit family in that dressing room and we will continue to be until the end of the season.
"We are not there yet but that has been a massive boost for us today and we have showed what we are all about."