A spirited Woking did their best to rain on Town's parade in wet, gloomy conditions at The Shay.
Pete Wild was yet to see a Town team score against Woking in three previous meetings, but Hyde's goal ensured The Shaymen go into the weekend's double-header with a crucial win under their belts.
It was better from The Shaymen after Saturday's underwhelming defeat to Bromley, but they'll need to play better still against Stockport.
Jeff King's suspension saw Jamie Allen starting at right wing-back, Tom Bradbury replaced Niall Maher, Jack Senior came in for Danny Williams and there was a first start for Kian Spence in place of Kieran Green.
Town wanted to play out through Neill Byrne and Bradbury, but Woking were wise to it and closed down the two centre-backs aggressively.
Unlike against Bromley, there were gaps for Town to play into, and opportunities for playing through Woking, although the visitors worked hard to close Halifax down, not resembling a team with nothing to play for.
The Cards nearly took the lead when a free kick was headed goalwards and brilliantly saved by Sam Johnson, but the tap-in on the rebound was ruled out for offside.
Other than a free kick by Luke Summerfield that was glanced wide, The Shaymen had struggled to create much early on.
Halifax were utterly dominant, but couldn't transfer their possession into chances, with Allen getting into decent positions down the right but not coming up with an end product.
When Town did, with a superb counter-attack from a Woking corner involving Spence, Senior and Billy Chadwick, Hyde dragged his low shot wide across goal.
Then from the impressive Spence’s lofted pass, Hyde did well to get to within shooting distance but again fired off target.
Town were now building some momentum, with Woking starting to hang on as keeper Craig Ross reacted magnificently to tip Hyde's header over from a corner, before Bradbury headed wide from the next one.
Chadwick was next to go close with a low shot across goal, with The Shaymen playing much better than their previous outing, showing more energy and incisiveness, helped by Spence's display, with the midfielder constantly showing for the ball and looking for the forward pass.
There was a massive let-off for Byrne shortly before half-time when his short back pass let in the visitors, but Town somehow kept the ball out, with Senior the savior with a last ditch tackle.
It would have been harsh on Town, who had controlled the game.
Other than two clear chances, Woking had been penned in their own half, but for a side with only one clean sheet in their last eight games, had defended well, especially giant centre-half Moussa Diarra, constantly in the right place at the right time.
The Cards looked dangerous from set-pieces and long-throws, but were ineffective in open play.
There was no half-time bounce for Town, with Woking improving after the interval and making it more of an even contest.
The Shaymen's composure had deserted them since the restart as the game descended into a scrappy affair with attacks from both teams breaking down repeatedly.
Woking were picking Town off, winning the ball back when moves broke down and then trying to break up field. That led to a great chance for Zac Robinson, but he curled his shot wide from near the penalty spot.
Halifax had regressed in the second-half, getting bogged down in loose touches and sloppy passes, but Woking were growing in confidence and sensing they could get something.
But out of nothing, a wonderful pass by Summerfield played in Hyde, who beat the offside trap and was left with an easy finish from close range.
Substitute Kieran Green nearly made it two moments later but fired wide from just inside the box.
Johnson was forced into a good save from a drilled shot soon afterwards as Woking sought an equaliser.
Hyde nearly wrapped up the win when his header from a corner was cleared off the line, before The Shaymen weathered some late pressure in the incessant rain.
Halifax: Johnson, Byrne, Clarke, Bradbury, Summerfield, Spence (Green 64), Woods, Allen (Campbell 77), Senior, Hyde, Chadwick (Williams 89). Subs not used: Davison-Hale, Maher.
Scorer: Hyde (74)
Shots on target: 4
Shots off target: 12
Woking: Ross, Cook, Gerring, Diarra, Hamblin, Cooper, Ferdinand, Freeman (Hodges 57), Lofthouse, Robinson, Dalby. Subs not used: Skinner, Evans, Leslie, Smith.
Shots on target: 2
Shots off target: 2
Referee: Aaron Jackson
Town man of the match: Spence had a very good game on his first start, but Luke Summerfield provided a terrific assist for the goal and was a constant source of activity and effort in midfield.