The reverse fixture on the opening day of the season finished 33-33 and another draw was in the offing when Paul Brown-Bampoe scored a charge-down try for Chiefs in the 78th minute.
Saints were not to be denied, though, and a fine dummy by Smith saw him coast over the line to remain one point above Bath ahead of next weekend's clash between the top two.
"It's fine margins, but I like the way we carried on playing, carrying that pressure and having that belief," said Northampton director of rugby Phil Dowson.
Exeter got off to a dream start with a try after only 82 seconds from England flyer Immanuel Feyi-Waboso
Will Rigg added a second score with Henry Slade converting both for a 14-0 lead.
Northampton bounced back to level by half-time with England scrum-half Alex Mitchell and Ollie Sleighthome scoring tries.
Campbell Ridl restored Exeter's lead, but Feyi-Waboso's yellow card for a deliberate knock-on swung momentum back in Northampton's favour.
Smith's delicate little chip over the Chiefs' defence created a foot race for the line, won by George Furbank, with Smith converting to level once more 15 minutes from time.
Exeter went down to 13 men in the 73rd minute when Ridl stopped a possible try with illegal work at the breakdown, and from the tap penalty, space was created for replacement Henry Pollock to collect Saints' bonus-point touchdown.
Exeter were given a lifeline when Brown-Bampoe charged down a clearance kick and beat Furbank to the ball, with Slade converting magnificently.
Saints were not satisfied with a draw, though, and a break by Fraser Dingwall set up Smith to win the game.
Two bonus points did at least bolster Exeter's push for the play-offs despite slipping to fourth.
Bath had a much more comfortable afternoon as two first-half tries by Santi Carreras teed up a 48-15 win against Harlequins.
The 64-cap Argentina international, who started the game at full-back and finished at fly-half, also kicked a conversion as Bath ran in eight tries.
Tom Carr-Smith, Tom Dunn, Ewan Richards, Josh Bayliss, England flanker Guy Pepper and Bernard van der Linde were also on target.
Gabriel Hamer-Webb scored five tries as Leicester thrashed Newcastle 62-3 to climb up to third.