Having been sloppy all over the pitch in the first half and conceding a goal just before the half hour mark, the Shaymen tightened it up after the break and two impressive strikes gave them the points.
Campbell showed a cool head to level it up on the hour while Heslop's strike was all about power and precision as he lashed home in trademark fashion.
And they could even afford to miss a penalty, Jon Shaw having his kick saved after Scott Doe had been red carded for bringing down Campbell in stoppage time.

See the slide show from the game

But perhaps the most important thing about the game was that Halifax showed they have what it takes to bounce back from knocks, something they are almost certain to have to do again before the end of the campaign.
It could easily have been 2-2 inside the opening eight minutes of the game as both sides created opportunities.
Town had the first, Campbell laying the ball off for Heslop whose 25-yarder was saved at full stretch down to his right by Scott Henderson.
And four minutes later Craig Nelthorpe found Campbell on the left and he sent over a deep cross for Danny Forrest, whose volley was tipped over the bar.
In between, Nick Crittenden sliced horribly wide from a Scott Beavon cross and soon after Forrest's effort Adam Legzdins saved brilliantly from Tony Bedeau who got on the end of Crittenden's cross on the edge of the six yard box.
Forrest flicked a Nelthorpe free kick wide of the target and Henderson saved from Forrest with his legs after Shaw and Andy Campbell had combined to create an opening.
Having looked threatening in attack, but shaky at the back, Town found themselves behind in the 28th minute in controversial circumstances.
Marcus Browning was a yard offside when he picked up the ball on the right, but there was no flag and when the Halifax defenders failed to deal with the cross Anton Robinson popped up to stab home.
Bedeau had a couple of chances to increase the Terras' lead, but failed to take either, while Town struggled to rediscover the form they had shown in the opening 20 minutes.
The second half started slowly but burst into life in the 60th minute when Town levelled.
Legzdins started the move with a throw to Heslop who switched play to Forrest. His through ball picked out Campbell and, after taking the ball into the area, he fired home despite Henderson's touch.
Bedeau was inches away from restoring Weymouth's lead from a Jack Compton cross, but it was Town who started to gain the upper hand as they pushed for the winner.
Heslop fired a ball into the Terras' defensive wall after Anthony Griffith had been fouled and there was an almighty scramble in the 75th minute when Griffith's shot fell to Campbell whose effort was blocked.
The ball looped to Forrest who set himself before firing wide of the target on the right.
Town had to wait just three minutes for the goal that put them ahead and it was worthy of winning any game.
Shaw fed the ball to the left for Heslop, who drifted in from the wing before unleashing a right foot shot that flew over Henderson and dipped under the bar.
Weymouth's best chance to claim a share of the spoils came from a Bedeau header that Legzdins saved with ease.
And Town should have added a third goal in stoppage time after Campbell had raced clear.
He was challenged by Doe whose tackle was felt by most in the ground to have been well timed.
The referee was one of those who did not and produced a red card for the Weymouth defender but Shaw was unable to take his tally for the season to 19 when he had his spot kick saved by Henderson diving to his right.

STAR SHAYMAN
With so much at stake it was always going to be a difficult afternoon for the Town players.
But they responded as manager Chris Wilder knew they would and emerged with the victory they needed.
Andy Campbell has waited a long time to start a game and he made the most of his opportunity as he bagged the crucial equalising goal.
He was in the thick of it at the start of the game when Town could have taken an early lead and continued to pose a threat to the Terras' defence.
Simon Heslop drove the Shaymen forward - as we have come to expect - and his goal to win the clash was simply stunning.
There is a real sense of expectancy from the fans whenever he gets the ball around the edge of the area and he had tested the keeper early in the game.
Danny Forrest made a welcome return, looked sharp when he got the chance and was only denied an early goal by a fine save
Campbell takes the three points on offer in our season-long competition with Heslop getting two and Forrest one.

MATCH FACTS
Halifax Town: Legzdins, Doughty, Clarke, Wright, Davies, Forrest, Kearney (Griffith 53), Nelthorpe (Killeen 49), Heslop, Campbell, Shaw. Subs (not used): Quinn, Stamp, Whitehouse.
Booked: None
Sent-off: None
Goals: Campbell 61, Heslop 78.

Weymouth: Henderson, Critchell, Okuonghae, Swaibu (Doe 74), Challis (Weatherstone 84), Crittenden, Browning, Compton, Robinson, Bedeau, Beavon (Malcolm 70). Subs (not used): Matthews, Anzite.
Booked: Browning, Critchell, Weatherstone.
Sent-off: Doe (90).
Goal: Robinson 29.

Attendance: 971
Referee: P Quinn (Middlesborough).

PLAYER POINTS
Jon Shaw 36, Simon Heslop 32, Tom Kearney 21, Anthony Griffith 21, Andy Campbell 16, Lewis Killeen 14, Steve Torpey 12, Steve Bushell 10, Jake Wright 10, Matt Doughty 9, Daryl Taylor 8, Rob Scott 7, Danny Forrest 6, Adam Legzdins 6, Cortez Belle 5, Craig Nelthorpe 4, Tom Clarke 3, Craig Mawson 3, Nathan Joynes 2, Adam Quinn 1, Darryn Stamp 2, Ryan Toulson 2, Greg Young 2, Peter Atherton 1.

YOU SAY
A tactical inspirational masterpiece by Wilder in taking off Kearney. Griffiths drove us forward and we scored 2 good goals to win. Forrest ok on return - big stu

First half was as good as I've seen us play in 40 odd years. Second half was even better. Worth paying 15 quid just to see Heslop's goal - the taxman

After Wilder brought on Griffith we looked so much better. Campbell looked good, so did Forrest apart from finishing. We kept the ball on the ground in second half and it worked - anon

What chance do we have next season when Wilder is irresponsibly moaning about getting new players? - ronnie warren

Started playing when Kearney went off and won. Will Wilder learn the lesson? happy andy