Ivan Sproule's second-half goal took County to within two points of Inverness, who are currently occupying the second UEA Cup qualification place.
The two Highlands clubs meet on the final-day of the season, and Adams said: "It could be pivotal.
"We've got three difficult games now - Motherwell, Celtic and Inverness. The derby finishes the season and you don't know what will happen before then."
County might have scored more after United's Barry Douglas was sent off with 25 minutes to play, and Adams said: "We had the better of the opportunities and controlled the game. It was a very good performance and nice to get a home win.
"We hit the bar and got into very good positions but in the end Iain Vigurs had a moment of brilliance to chip a pass to Sproule and it was a very good goal.
"It was win or bust and I said to the players at half-time, 'you have to believe'.
"We're delighted we've been able to win and close the gap on Inverness and go above St Johnstone."