It brought a perfect end to a traumatic week for the cash-strapped Wiltshire club, whose future seems assured following the promise of a new year takeover.
Andrew Fitton, who was introduced to the County Ground crowd before the start, is set to buy the club in early January to alleviate Swindon's fears of being plunged into financial ruin.
Hartlepool had threatened to spoil the party by taking an interval lead, but Swindon scored twice in the second half as they secured a long-awaited League victory.
The win has prompted Swindon's caretaker-manager David Byrne to make a Christmas Eve approach to Reading boss Steve Coppell to extend the loan period of striker Simon Cox.
"Simon's been with us for four months now, since early September, and has scored eight goals in that time," Byrne explained.
"But he's due to go back to Reading after the Swansea game here on January 1st. I think it will be mutually beneficial if he stays here and gets regular first-team football, especially after his outstanding performance today."
Cox helped to kick-start Swindon's second-half recovery, after they had been facing a fourth straight defeat when Ian Moore bundled Hartlepool in front just before half-time.
Swindon had been guilty of giving away a string of free-kicks in the danger-area outside their own penalty area during the first-half - and paid the penalty shortly before the break.
The impressive Godwin Antwi met a free-kick from Robbie Elliott at the far post and fired it across the face of the goal for Moore to plunder his eighth goal of the season.
But Hartlepool's vulnerability on their travels cost them a sixth successive defeat.
As Swindon raised their game, so the visitors' defence creaked - Cox equalising three minutes into the second half from an excellent pass by Frenchman Miguel Comminges.
With 18 minutes remaining Swindon grabbed a deserved winner. Michael Nelson upended Corr and the Irishman drilled the winner into the top right-hand corner from the spot.