The Glovers had won ten of their previous 12 home games, so victory at Huish Park is no mean feat for The Shaymen, who had to contend with horrible conditions and were flattered by the scoreline in a match much closer than the result suggests, but they produced a classic away performance to secure three precious points.
There were shots from range by Reuben Reid and Martin Woods early on, but soon enough the blustery wind took control of the game, severely hampering both teams.
The windy conditions meant lofted passes from Town struggled to reach halfway, and set-pieces and goal kicks took twice as long to take due to the ball being blown off their mark.
Such conditions meant it was never going to be a classic, especially coming only 48 hours after both teams' previous games.
But Town got their noses in-front when a lovely through ball by the returning Tom Bradbury played in Billy Chadwick, who replaced the injured Jamie Allen, and after he was tripped, Summerfield confidently swept in the resulting penalty.
Now Town had the lead, the wind was doing an extremely effective job in disrupting the flow of the game and preventing Yeovil applying any real pressure.
There was a header wide by Billy Sass-Davies from a corner, but the conditions permeated every aspect of the contest, rendering passing, control and dead ball situations highly unpredictable and, at times, impossible.
It was an ugly, scrappy contest, littered with mistakes. When there were decent passages of play, they stood out a mile, with Woods catching the eye due to his calm head, vision and awareness among the maelstrom.
Nathan Clarke impressed too, standing strong against striker Joe Quigley, with the Town defence rarely troubled.
It was a test of Town's desire, how much they wanted to fight the wind and rain and do the hard yards, but they dug in.
The Shaymen were pressed back for spells, not helped by the fact they couldn't get out of their own half from goal kicks due to the wind, but Yeovil failed to turn their territorial advantage into chances.
Halifax had looked a little shaky at the back early on, but as the opening half went on, the visitors adapted to the conditions, and Yeovil looked increasingly unlikely to equalise.
A spectacular shot by Reid nearly did a couple of minutes after half-time, but it struck the inside of the post and bounced back to Sam Johnson.
Tom Knowles then curled a free-kick just wide of the opposite post, with the hosts much sharper and showing more urgency since the restart.
Johnson did very well to keep out Knowles' free kick from almost an identical position a few minutes later, with Yeovil the better side.
The Glovers looked a threat every time they went forward, and Town had started to look vulnerable at the back again, with Clarke nearly scoring an own goal but for Johnson's quick reaction to his miscued clearance in the box.
Town switched to a back three midway through the second half, having weathered the other storm that Yeovil had produced since the interval.
The hosts' screams for a penalty for holding on Quigley at a corner were ignored, but Yeovil were struggling to create after that earlier flurry of chances and were getting frustrated.
They were fuming when another penalty shout, for a foul on Reid by Niall Maher, was rejected, and then moments later, Summerfield's shot was parried and Green bundled in the rebound to seal the win.
Substitute Hyde added the gloss in stoppage time when he raced onto a loose header from a Yeovil defender and coolly slotted under the keeper.
Yeovil: A Smith, Kelly, Skendi (Hunt 86), Davies, Dickinson, Knowles, J Smith (Bradley 74), Dagnall (Sonupe 85), Neufville, Reid, Quigley. Subs: Evans, Stephens.
Shots on target: 4
Shots off target: 6
Halifax: Johnson, Byrne, Clarke, Maher, Bradbury (Hyde 68), King, Green, Summerfield, Woods, Williams, Chadwick (Stephenson 79). Subs not used: Davison-Hale, Senior, Spence.
Scorers: Summerfield (16), Green (85), Hyde (90)
Shots on target: 6
Shots off target: 2
Referee: Elliott Swallow
Town man of the match: Martin Woods and Luke Summerfield were both excellent in central midfield, as were Nathan Clarke and Niall Maher at the back. Clarke gets it for a superb display of blocks, clearances and interceptions.