Centre-back Collins attempted to clear a harmless ball from Vale substitute Chris Birchall, but only succeeded in slicing it over his own goalkeeper Lee Nicholls from 12 yards.
Vale's vastly superior goal difference to challengers Cheltenham means Micky Adams' team will be playing in npower League One next season while the Cobblers will be in the play-offs.
A carnival atmosphere before kick-off quickly turned sour for more than 11,000 Vale fans when the visitors took a third minute lead.
Ben Harding's right-wing corner found its way to the far post where Clarke Carlisle forced the ball in with a left-foot shot from four yards.
It was the visitors' first goal for 368 minutes, but they were soon close to a second when a slip by Liam Chilvers almost left Luke Guttridge in the clear.
Vale gradually got on top but Guttridge should have taken a simple chance in the 34th minute when he cracked a six-yard shot against the crossbar.
And that proved a turning point as Chilvers equalised after the Northampton defence failed to clear their lines from Jennison Myrie-Williams' 39th minute corner.
Tom Pope lifted a clever ball back into the six-yard box and Chilvers steamed in at the far post to bury a downward header past Lee Nicholls.
Darren Purse's header was cleared off the line by Lewis Hornby as Northampton buckled as half-time approached.
But the visitors regrouped after the interval and a sublime 20-yard finish by Roy O'Donovan, who curled the ball high inside Chris Neal's right-hand post in the 69th minute, looked to have won it until Collins' late gaffe.
- Sports & Recreation
- Lee Nicholls
- Liam Chilvers
- Chris Birchall