Regan Linney’s 20th goal of the season was enough to clinch the points for the Blues at The Shay.
His strike capped an all-round effort against play-off chasing rivals which left head coach Hughes delighted.
“It was really satisfying,” Hughes told the News & Star.
“You come to these places when it's a bit bleak, blowing a gale and horizontal rain, and you have to set your stall out really early on.
“I thought that's exactly what we did, and we continued that for the full 90-odd minutes.
“It was a really good away performance. I can't really criticise the guys for anything. I thought they were really resilient, worked exceptionally hard for each other, had a good shape and a good understanding of what we were trying to do in comparison to the opposition.
“It was one of the more pleasing performances and results.”
Linney got the only goal in the 68th minute as he ran onto a pass from the recalled Jack Ellis.
Carlisle then dug in for a clean sheet on an evening of miserable wet and windy conditions in Yorkshire.
It saw United retain their four-point advantage in third place, with six games to go.
Regan Linney hit the winner at The Shay with his 20th goal of the season (Image: Richard Parkes)
Linney reached the 20-goal milestone in his 40th appearance of the season.
Hughes hailed the Blues’ top scorer and said: “When chances are created, you want Regan involved.
“More often than not, he will at least test the keeper – and often he scores.
“He's shown a little bit more form now. He had a spell where he was a little bit below what he'd been able to produce, because he was outstanding earlier in the season, but he's now looking like he's coming back to form, and his general play is really good as well.
“His defensive work was excellent – we demand that of him, and he understands that now, and we're getting more complete performances from him.
“[Reaching 20 goals] is a feather in his cap, and for him to come to a new club, a bigger stage and bigger demands, to produce what he's produced up to this point – and there's more to come, we think - yeah, credit to the kid.”
Hughes felt the way Carlisle applied themselves against Adam Lakeland’s seventh-placed Halifax was critical to the victory.
“I think it was just the intent we showed,” he added.
“I thought straight from the off it was about us and what we needed to do, and everyone bought into that and understood exactly that it was going to be a difficult night if we didn't all work hard, stick together, and make sure we capitalised on the big moments in the game, which we were able to do.
“As an away performance, that was as pleasing as we've had.”
Terell Thomas cleared a Halifax chance off the line shortly before Linney struck (Image: Richard Parkes)
Among the other players to come in for praise was midfielder Alex Gilliead, who was impressive throughout.
“He's a very experienced player, and the qualities that I know he's got and I see in his play week-in, week-out, are sometimes underestimated by people, but I think in this game everybody understood what he gives the team.
“I thought he was excellent in the first half, getting on the ball for us, having that confidence in his own ability to dictate from that deeper position, and in the second half he had to dig in like everybody else.
“He was great at that as well, but it wasn't a surprising performance because that's what I get week-in, week-out from Gilly.”
United stood up to Halifax’s attempts to fight back and Hughes added: “They never really had huge spells of momentum where we were totally under the cosh.
“They got the ball out wide a couple of times and tried to get balls into the box, but even when they were able to do that, I thought defensively we defended our 18-yard box really well.
“I think everybody came out with flying colours.”
Hughes said Bevis Mugabi was left out after feeling some discomfort in his knee, United opting not to risk the centre-back as Terell Thomas came in.
Ellis was also recalled at right-back in place of Hayden Atkinson, Hughes saying he felt it was right to give teenager Atkinson a breather after his impressive first run of league appearances.
Carlisle remain four points clear of fourth-placed Boreham Wood, who won 2-1 at Aldershot Town. The Blues' place in the play-offs is now all but confirmed, and will be mathematically certain if ninth-placed Hartlepool United fail to win at Morecambe tonight.
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