Matt Calland's side, who now sit just a point behind Salford and three clear of third-placed Sheffield on the league ladder after five rounds, looked down and out when they slipped 36-10 behind with 25 minutes remaining.
But a James Haley touchdown 23 minutes from the end sparked a remarkable sequence of events, with Fax scoring five tries to complete a brilliant comeback against a Centurions outfit that had been a man down since the dismissal of substitute Chris Hill for a horror tackle on Fax prop David Wrench just before the half hour.
It was an exhilarating end to an afternoon that had looked like being eminently forgettable as Fax stumbled badly after Sean Penkywicz had given them fifth-minute lead with a darting solo score straight from the scrumbase.
Fax's defensive door has been creaking practically from day one this season, but it was hanging off its hinges for long spells at Hilton Park as the home side, inspired by veteran full back Dennis Moran and the intelligent promptings of Fax old boy Ian Watson at scrum half, ran riot.
Hooker Dave McConnell had eclipsed Penkywicz's opener within three minutes, and Leigh - under the temporary tutelage of Paul Rowley - underlined their early superiority by hitting Fax with back to back tries just after quarter time.
Wingman David Alstead got the first after a superbly judged Lee Marsh kick straight from a scrum deep in their own half, before Moran dived in, starting and finishing a move down the right that featured centre Toa Kohe Love.
Watson converted two of the three for a 16-6 advantage and even Hill's red card for attempting to decapitate Wrench, the worst of a handful of questionable Leigh tackles, could not halt the momentum.
The young forward had only been off the field a matter of a few minutes when loose forward Mike Wainwright capped a try typical of the afternoon: Fax making the initial error, in this case Penkywicz throwing a pass that was picked off by Lee Doran, compounding it with a clutch of missed tackles and the home side showing the skill and enthusiasm needed to capitalise.
Watson converted for 22-6 and added an injury time penalty for 24-6 before Fax, already with a concussed Andy Smith, a semi-conscious Wrench and a limping Paul Southern cluttering up their dugout, suffered a further setback when Graham Holroyd was sin-binned for persistent holding down.
Things could hardly have got worse at that point, and when Kohe Love put down a sitter on the line a couple of minutes into the second half, the omens were still not great.
Lee Patterson's blistering finish in the right hand corner, after a scything Shad Royston break, gave Fax some respite at 24-10, but another double dose of misery, Alstead going in after Marsh and Kohe Love produced great passes on the right and Chris Giles applying a routine finish on the opposite flank after a flowing move straight from a scrum, left the visitors looking dead in the water at 36-10.
One thing this Halifax side do not lack though is self belief and, belatedly, that slowly began to show on the field.
Haley, so impressive again, scythed through after another top performer, Paul Smith, supplied the ammunition, Holroyd's boot making it 36-16.
The visitors should have been in again immediately, Jon Goddard sending Lee Patterson haring away down the left only for the winger's pass to the supporting Miles Greenwood to end up some way above the head of its intended target.
The optimists in the crowd had their fanciful ideas of a comeback encouraged by another try, Holroyd skipping through after Penkywicz had torn his hometown club to shreds down the right, leaving Fax trailing 36-22.
At that point, something, somewhere clicked in the minds of both teams: Fax looked like a side that had just realised victory was still possible, while it seemed to dawn on Leigh that their position was not quite as unassailable as they had thought.
What followed was simply brilliant, at least for Fax's hardcore travelling support, some of whom were presumably reassessing their decision to boo the players from the field at half time.
Damian Gibson scooted in after Penkywicz, Royston and Greenwood had ripped Leigh's left side defence to bits, Greenwood showing great composure to deliver the killer pass, and Holroyd kicked Fax into range at 36-28.
The visitors marched downfield again, Holroyd's towering kick being taken by Haley before Moran went in high on Wrench. That gave Fax the extra posession they needed, Penkywicz forcing his way over under the posts from point blank range and Holroyd cutting the gap to 36-34.
Fax still needed the sharp eyes of a touchjudge to keep their comeback on the rails, the man with the flag pointing out to referee Craig Halloran that Leigh's Gareth Price had come from an obviously offside position when he fell over the line with eight minutes to go.
Calland's men then delivered the coup de grace, Paul Smith storming in after Greenwood, enjoying his best game of the year against his former club, had broken clear again.
Some great defence from Goddard, Patterson and Richard Varkulis then forced Alstead back into his own in goal, and when Marsh's drop out sailed out on the full, Holroyd stepped up to establish a crucial six-point gap.
Fax still had to see out five minutes of injury time, but they did so comfortably enough while Leigh were lucky to finish with 12 men after Kohe Love's ugly challenge on Janan Billings.

MATCH FACTS
Leigh: Dennis Moran; Chris Giles, Adam Thomas, Toa Kohe Love, Dave Alstead; Lee Marsh, Ian Watson; Mike Morrison, Dave McConnell, Gareth Price, James Taylor, Lee Doran, Mike Wainwright. Subs: Mark Roberts, Aaron Smith, Chris Hill, Andy Hobson.
Tries: Moran, Alstead (2), McConnell, Giles
Goals: Marsh, Watson (5)
Sent off: Chris Hill, 29, high tackle
Sin bin: Dennis Moran, 3, professional foul

Halifax: Shad Royston; Lee Patterson, Jon Goddard, James Haley, Andy Smith; Graham Holroyd, Sean Penkywicz; Paul Southern, Janan Billings, Dana Wilson, David Larder, Richard Varkulis, Paul Smith. Subs: Damian Gibson, Miles Greenwood, David Wrench, Frank Watene.
Tries: Patterson, Gibson, Haley, Holroyd, Penkywicz (2), P. Smith
Goals: Holroyd (7)
Sin bin: Holroyd, 40, holding down
Attendance: 2,212
Referee: Craig Halloran

STARMAN
For 40 minutes yesterday you would have struggled to pick a Halifax man of the match. In the last 20 minutes, you could probably have named any one from 13.
Paul Smith was one of the few players to figure equally prominently in both halves, playing 80 typically effective minutes in the back row of the pack.
Smith was instrumental in the James Haley try that kick started Fax's revival and generally looked a class act from start to finish, both with, and, more importantly, without the ball.
Haley takes the two points after another strong performance that underlined his return to form.
Haley came up with a couple of slashing breaks, scored a crucial try and worked as hard as anyone, even when things weren't going Fax's way.
Crucially, he also showed great composure to deal with a brace of tricky short restart kicks as Leigh looked to regain possession late in the game.
Without those, the result might have been very different.
The final point goes to Fax's super sub, Miles Greenwood, who came off the bench to add some real punch to his team's attacking game.
Greenwood, the subject of some harsh terrace criticism in recent weeks, produced a couple of breaks that led to tries and, just as importantly, showcased the footwork that is a key part of his game.
Greenwood, more than anyone in the Fax camp, must be hoping for the hard, dry grounds of summer.

PLAYER POINTS
Paul Smith 10, James Haley 10, Sean Penkywicz 9, Graham Holroyd 8, Craig Kopczak 8, Andy Smith 8, Lee Patterson 7, Shad Royston 5, Paul Southern 4, Jon Goddard 4, Mike Ratu 3, Dana Wilson 3, Dave Larder 3, Frank Watene 2, Andy Gorski 2, Mick Govin 2, Janan Billings 1, Miles Greenwood 1

YOU SAY
Great win and good performance Fax. - Grebbo

Speechless. James Hayley class. Well done Fax - Amy E

Can't believe that. Still buzzing! What a comeback Fax, great effort! - Pete 'the taxman' Ryan

Wow Fax. What a second half. Well done. - Shaz

What an absolutely brilliant second half - never gave in. Get in there ! - Ackers

Unbelievable. Amazing comeback! -Clare, Brighouse

STAT ATTACK
Leigh
First half
Completions: 17/22
Penalties: 7
Second half
Completions: 12/16
Penalties: 3

Halifax
First half
Completions: 15/22
Penalties: 8
Second half
Completions: 15/20
Penalties: 4