All-rounder Sales, the 18-year-old son of former Northants batsman and skipper David, struck a sublime 53 off 120 deliveries on his second red-ball appearance to lead a gritty final day rear-guard.
Luke Procter scored 44, while unbeaten Simon Kerrigan ate up a heroic 135 balls for his 28 not out as the County edged into a lead with 10 overs to spare, with Kerrigan going on to make sure his side avoided defeat in David Ripley's final home game as head coach.
Durham had taken wickets throughout the day, with Matty Potts taking four for 48 – to return career-best match figures of eight for 90 – but he nor his attack partners could find a complete set as Northants reached 230 for nine at the close.
After a washed-out day three, Durham required 10 wickets, Northants needed to bat out the day or wipe out a 217-run deficit and not leave enough time for any chase.
Emilio Gay survived a spill at third slip and a strong lbw appeal but was snatched at second slip when trying to work Potts into the legside.
Ricardo Vasconcelos edged behind to give Rushworth his 55th Championship wicket of the season – the sixth time he has reached that figure– before Rob Keogh was adjudged lbw to Ben Raine.
The resumption from lunch saw a showcase of quick bowling from Potts and Rushworth on a largely unresponsive pitch as three wickets fell in 40 minutes.
Potts secured a nick behind when he angled across the left-handed Saif Zaib and then produced a gem to kiss the surface and Adam Rossington’s outside edge, with David Bedingham clutching on at first slip.
Harry Gouldstone was caught on the crease as Rushworth cannoned into the top of off stump – with 106 still needed to make Durham bat again.
Throughout the quick succession of wickets Luke Procter had stood firm, as he had for his 76 in the first innings. But after a half an hour lookout with James Sales, he was plumb lbw to a full Raine delivery for 44.
Sales and Kerrigan set up camp and added 68, with a volley of boundaries off the former’s bat flying after tea, while equally importantly eating up 187 balls.
Sales reached a maiden first-class fifty with a three through midwicket off 99 balls. Potts struck with his second delivery with the second new ball when Sales toed a pull to mid-on.
Kerrigan and Sanderson took the hosts into the red but with 54 balls remaining the latter was leg before to Scott Borthwick but Kerrigan marshalled Jack White through the final few overs of the match to secure a thrilling draw.