Mark Shelton had given Hartlepool a first-half lead, and it looked like Town would be frustrated in their efforts at getting back level until Green's header 12 minutes from the end.
Halifax then had Danny WIlliams sent-off, making for a nervy finish in Town's first home game for 31 days as the fixture was finally played at the fourth time of asking.
Combined with the superb win a Torquay, four points from these two games represents a very good return.
And while Halifax's performance levels didn't reach those at Plainmoor, they deserve credit for their persistence and perseverance.
Town were caught out with a short corner, which was quickly worked to the unmarked Shelton just inside the box, who swept the ball across goal and in.
A minute earlier, Jamie Allen got on the ball in space to the right of the Hartlepool box but his cross flashed through the area without a touch.
The visitors looked more fluid and smooth in possession, and were comfortable and confident on the ball.
Right wing-back Jamie Sterry, impressive on Boxing Day in the reverse fixture, again caught the eye with some bursts down the right flank, while the Pools midfield offered good runs forward from deep and linked play effectively.
Town found it more difficult to build attacks and thanks to some unforced errors, took a while to get going.
Green was his usual tenacious self in midfield, but Town struggled to penetrate Hartlepool's back three. Allen and Jeff King looked their best outlets down the right, but few chances were created.
Just as Pete Wild had left his seat in the East Stand to confer with Chris Millington over the advertising hoardings, Jack Earing hit the inside of the post with a superb shot, with Hartlepool defender Lewis Cass reacting brilliantly to clear the rebound for a corner.
That was the first real effort of note from The Shaymen, 25 minutes in, and the hosts were yet to bring a save from keeper Ben Killip by half-time.
Tahvon Campbell was showing some decent touches down the left of a three-pronged attack, while Jake Hyde, making his first start since December 15, looked lively but didn't see much of the ball.
Hartlepool didn't really build on their lead, although Cass forced Sam Johnson into a decent save, with the visitors not retaining the ball with the same assurance as the first-half went on.
Halifax grew into the half, with Tom Bradbury heading just wide in added time, but still hadn't produced a prolonged spell of pressure by the break.
Neither side had been brilliant, but Hartlepool had done enough, getting the early goal and then protecting it.
Cass produced another terrific block shortly after the restart to prevent a shot on target, as Town started the second half with more urgency. They needed to maintain it.
Only an astonishing save from Johnson at point blank range prevented Luke Armstrong from doubling Hartlepool's lead though a few minutes into the second-half.
Town hunted the ball down but struggled to get it back at times as Hartlepool passed it around calmly, taking the sting out of their hosts.
Campbell wasn't having much input down the left, while Hyde still wasn't seeing enough of the ball, never mind getting chances inside the box. Without the creative force of Luke Summerfield, Halifax's attacks lacked that conduit and that incisive pass.
Still Killip waited to be tested.
Armstrong flashed a shot across goal and wide on the break for Hartlepool, with a second goal for the visitors enough to end the contest.
But Green's header dragged Town level as he nodded in King's superb free-kick from near the left touchline.
Gavin Holohan then blazed wide from inside the box as the match came to life.
As the contest sprang into an end-to-end game, substitute Williams was then sent-off for denying a goalscoring opportunity as Hartlepool broke upfield on a counter-attack.
If Town might have taken a point before kick off, they certainly would now as Hartlepool pressed for a winner.
Substitute Tom Crawford had a chance to win it for Hartlepool after a lovely one-two, but his tame shot was straight at Johnson.
Halifax: Johnson, King, Byrne, Bradbury, Senior (Woods 77), Green, Maher, Earing, Campbell (Williams 69), Allen, Hyde (Tear 95). Subs not used: Renshaw, Benn.
Scorer: Green (78)
Shots on target: 1
Shots off target: 9
Hartlepool: Killip, Sterry (Bloomfield 69), Odusina, Cass, Liddle, Ferguson, Shelton, Featherstone, Holohan (Crawford 82), Molyneux (Oates 56), Armstrong. Subs not used: Grey, White
Scorer: Shelton (13)
Shots on target: 5
Shots off target: 4
Referee: Garreth Rhodes
Town man of the match: Sam Johnson. But for a fabulous save while Town were trailing, The Shaymen may not have got a point.