Chris Burke's deflected strike and further goals from the impressive Keith Fahey and substitute Nathan Redmond stretched Birmingham's unbeaten run to 15 games in all competitions as they won 3-1.
Craig Davies' 10th goal of the season had brought Barnsley level and although the Tykes striker also hit the crossbar, Hughton's team were good value for their fifth consecutive away victory.
The three points leaves Birmingham five points behind second-placed Southampton with a game in hand, but Hughton is not getting carried away in a marathon season which has already seen his side play 44 matches.
The former Newcastle boss said: "I think we always have to kick ourselves and remind ourselves there is still a third of the season to go. I'm quite sure in that 15 games there are going to be lots of twists and turns.
"We're in good momentum but it's not only us. Blackpool lost tonight but there is a good group of teams who are all showing good momentum. The important thing for us is that we can't take our foot off the pedal.
"We've also got two teams above us who at this moment don't look like losing a game. I certainly think that any team that finishes above West Ham and Southampton will go up automatically."
Hughton was impressed the performance of his side and felt they were worthy winners.
He added: "I think it's an important win for us, I thought we deserved the win over the 90 minutes but we had to defend very well at times. I think that was the basis that allowed us to take our chances and go on and win the game."
Barnsley boss Keith Hill was aggrieved with a first-half decision that saw Matt Done flagged for offside when he raced clear of the defence and slotted the ball home.
The Birmingham defence had long since stopped when Done tucked the ball home, but Hill was frustrated with the decision as had the goal stood his side would have been level at 2-2.
Hill said: "I'm disappointed with the first goal, it was avoidable again and an individual error. The second goal was a very good goal, can't complain about that. But we had a major decision that the linesman got wrong and he didn't just get it wrong, he got it seriously wrong.
"I've watched it on the DVD, Matty Done is four yards onside. It's not marginal, Craig Davies isn't offside, Craig Davies doesn't touch, if Craig Davies touches it Matty Done is still onside. So they've made a major error that could have altered the outcome of the game."
Hill saw enough from Birmingham to suggest they have what it takes to return to the top flight at the first time of asking.
He added: "They've got a great chance, it's getting down to the nitty-gritty now with respect to the top three or four.
"They've got that knowhow when it come to the last five or six games of the season, they've all been there before so you can't argue that they're in there with a real good chance."
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