A Richard Brittain penalty was all that separated the sides in a hard-fought encounter at Dens Park as the Staggies moved up to fourth in the table on six points, level with Dundee United and only a point behind Celtic and Hibernian.
The result also extended the Highland club's impressive unbeaten run in league football, which now stretches to 38 games - their last defeat a 5-1 loss to Hamilton at the start of last season.
Staggies boss Adams, whose team has only conceded once in four matches, said: "The 38 games is a great record to have and it's brilliant to also have six points on the board in the SPL, especially after a difficult opening run of games against Aberdeen, Motherwell, Celtic and Dundee.
"It's terrific that Ross County can do so well in the Premier League but we've got a long way to go."
The talking point of the match came after 71 minutes when Mark Corcoran was brought down in the box by Neil McGregor and referee Steven McLean pointed to the spot.
Adams felt it was the correct decision, adding: "It was a clear penalty. We got in behind the right back and then across somebody else. You just can't dive in when you are in the box.
"It was unfortunate for them and you are always disappointed when you concede a penalty but looking at it, I thought it was a definite penalty.
"We created a number of opportunities in the first half and we were unfortunate not to go in at the break ahead, especially from the corner kick where we hit the woodwork.
"They hit the post as well on a counter attack but overall it was a strong performance from us and I think the three points were quite deserved."
Dundee manager Barry Smith, though, was unconvinced, but said afterwards that he was refusing to "get involved with the referee".
But Smith, whose side have picked up just one point from their opening four matches and are yet to score in the league, felt they deserved more from the match.
He said: "I definitely believe that we were worth more than worth a point.
"I thought we controlled the game for long spells. I think our final ball and some of our passing can be better in the final third but I can't fault the boys for effort and work-rate.
"That alone won't win games for us and we have to be better. The boys are working hard and putting people under pressure but it is the final ball that is letting us down. We are having a lot of possession but not doing a lot with it."
Smith handed former Hibernian striker Colin Nish a debut and although he failed to score, Smith was impressed with what he saw.
He added: "Colin is an experienced pro. He looks to link up and is good with the ball at his feet. He will definitely be a good addition for us."
