First-half goals from striker Jordan White and defender Alex Iacovitti took the Highland club into tenth place and with two league games remaining they are one point above Kilmarnock and three ahead of bottom side Hamilton, whom they host on Wednesday week before they take on Motherwell on the final day.
A delighted Hughes said: "The word I'm using is courage. You have to stand up and be courageous.
"We made two or three changes to freshen it up. We're asking guys like Michael Gardyne and Iain Vigurs to keep going and going to the end.
"All credit to these guys who know what Ross County is all about, they are giving it everything they've got and even the substitutes have a massive part to play.
"I hope we've timed it right, it's going to go right down to the wire. It's in our hands, I'm not interested in what's going on elsewhere.
"We've had results to give ourselves a chance to stay in the league.
"The inconsistency is frustrating when you see that performance today.
"We've given ourselves a chance and that's hopefully a big step towards staying in the league.
"But we're playing against a Hamilton team off the back of a good win and know how to stay in the league.
"It's not going to be easy. Hopefully we can play like we did here and that will be good enough to get us the win."
United failed to build on their impressive 3-0 win over Aberdeen at Pittodrie in the Scottish Cup last week.
Manager Micky Mellon admitted it was a "frustrating afternoon" but was reluctant to suggest next week's semi-final against Hibs at Hampden Park was a distraction.
He said: "I have been asked about that and it is a difficult one.
"It would be easy for me to stand here now and say it was a distraction.
"That would be the easy answer but we spoke all the time this week about fighting hard to not allow any excuses to come our way and say it was a distraction.
"We wanted to be a team who can put two performances together and a team that can adjust and adapt to what the game is saying to us. But we weren't able to do that.
"I keep coming back to it, it was two really poor goals which is always going to make it really difficult for ourselves but there was a lot of time after that and a lot of things that disappointed us.
"We can't dwell on it, we have to move on with lessons learned."