Town were far from their best, and a shadow of the side from their last two outings, but still got the win.
It marks a terrific week for Pete Wild s men after victories over Wealdstone and Notts County. This was without doubt the hardest earned of the three, and while Halifax didn't hit the heights here, they deserve credit for digging in and finding a way to win.
Mitch Hancox hit the post with a low shot after quarter of an hour, putting the stamp on Solihull's impressive start, and leading Pete Wild to leave his seat in the East Stand and talk tactics with Chris Millington on the touchline.
Jamie Ward then hit the bar, possibly helped on its way by Sam Johnson, with a curling effort from 20 yards as Solihull just lacked the goal to cap their spirited display.
New manager Mark Yates couldn't have asked for much more just two days after being appointed.
Halifax were flat, like all the life had been sucked out of them. The intensity and commitment that imbued their play against Wealdstone and Notts County conspicuous by its puzzling absence. Was it one game too many?
It was finally better from Town when Jake Hyde laid the ball off to Jack Earing, who then found Danny Williams on the overlap, but his low shot is saved by Ryan Boot.
But that wasn't turned into any spell of pressure, prompting more discussions between Wild and Millington over the advertising hoardings as Town struggled to impose themselves on the game.
The Shaymen's passing was off, there wasn't the same care or precision in possession as there had been in recent games and they looked a little unsettled by Solihull's start.
The visitors were aggressive, in Town's faces, closing down and full of energy.
Their passing was far slicker, their movement far better; anyone would have thought it was Halifax coming into the game having been stuffed 5-0.
It didn't help that Kieran Green was off it too, giving the ball away and lacking the usual spark to his play.
Nor did it help that Hyde was forced off injured a few minutes before half-time.
But two minutes after the restart, Woods converted from the spot after Jeff King was shoved over in the box.
Solihull had a penalty appeal of their own turned down shortly after when Reiss McNally went down in the Town box.
The pattern of the game remained though, with Town failing to get into a rhythm and Solihull's determination undimmed.
Halifax switched to 4-2-3-1 to try and impose themselves more, bringing on Jamie Allen and deploying him and Billy Chadwick either side of substitute Tahvon Campbell.
Only Solihull's lack of cutting edge in the final third let them down, with Nathan Cameron's header from a corner saved by Sam Johnson, but the visitors' effort couldn't be faulted.
Similarly for Halifax, they weren't firing going forward, but defensively they remained solid, with Niall Maher and Tom Bradbury alert and resolute.
Campbell switched with Chadwick and went to the left, but it was in defence where it mattered for Town. The hosts looked unlikely to score again, so couldn't afford to switch off for a second.
Halifax's attacks were now going from back-to-front, with any build-up play or passing through midfield abandoned.
The Shaymen's slender lead looked paper thin when substitute Kyle Hudlin, scorer of a wonder-goal in the reverse fixture, played in Ward, whose shot was superbly cleared off the line by Neill Byrne, and then Hudlin inexplicably put the rebound wide from five yards.
A crashing shot then flew just wide from Solihull as Town clung on.
Halifax: Johnson, Byrne, Maher, Bradbury, King (Allen 61), Woods, Green, Earing, Williams, Hyde (Campbell 37), Chadwick. Subs not used: Renshaw, Clarke, Tear.
Scorer: Woods (47)
Shots on target: 4
Shots off target: 6
Solihull: Boot, Coxe (Archer 85), Cameron, McNally, Cranston, Maycock (Hudlin 68), Ball (Usher-Shipway 79), Storer, Hancox, Ward, Rooney. Subs not used: Gleeson, Piggott.
Shots on target: 4
Shots off target: 8
Referee: Aaron Jackson
Town man of the match: Niall Maher, led Town's rearguard well with some good blocks and aerial clearances.