Northampton edged past Exeter 18-15 at Sandy Park on Sunday to move back into the Aviva Premiership play-off picture.
The home fans were scenting a famous victory that would have sealed a top-four finish for the Chiefs as they went into half time 10-3 ahead.
However Northampton, with the wind behind them, scored second-half tries through wingers Chris Ashton and Paul Diggin to climb above the Chiefs in the table with one match remaining.
Exeter claimed a losing bonus point at the death with a try from Richard Baxter. But they face a far tougher final fixture against third-placed Saracens at Vicarage Road while Saints entertain Worcester Warriors.
Stephen Myler kicked the Saints ahead after some early pressure but a quick-tap penalty from Haydn Thomas created the momentum for Gonzalo Camacho to burst through a couple of tackles and lunge over the line.
Ignacio Mieres converted and added a penalty as the Chiefs grew in authority in front of their home fans and a favourable first-half wind.
However Northampton hit back straight after the break with Ashton flying in at the corner following a neat wrap-around move in midfield and slick passing out to the right flank.
Meires pulled a penalty effort left of the uprights from long-range, while Myler landed simple penalty with 17 minutes remaining to edge Saints in front.
And with six minutes remaining Diggin scarpered over in the left corner after a powerful Saints scrum won the ball against the head.
Myler's added the touchline conversion before Baxter burst over in the last minute to grab the bonus point.
Tries: Baxter, Camacho
Tries: Ashton, Diggin
Pens: Myler 2
Exeter: 15 Phil Dollman, 14 Gonzalo Camacho, 13 Bryan Rennie, 12 Jason Shoemark, 11 Matt Jess, 10 Ignacio Mieres, 9 Haydn Thomas, 8 Richard Baxter, 7 James Scaysbrook, 6 Tom Johnson, 5 James Hanks, 4 Tom Hayes (capt), 3 Hoani Tui, 2 Chris Whitehead, 1 Ben Moon.
Replacements: 16 Neil Clark, 17 Brett Sturgess, 18 Chris Budgen, 19 Aly Muldowney, 20 Ben White, 21 Kevin Barrett, 22 Gareth Steenson, 23 Sireli Naqelevuki.
Northampton: 15 Ben Foden, 14 Chris Ashton, 13 George Pisi, 12 James Downey, 11 Paul Diggin, 10 Stephen Myler, 9 Lee Dickson (capt), 8 Roger Wilson, 7 Phil Dowson, 6 James Craig, 5 Christian Day, 4 Mark Sorenson, 3 Brian Mujati, 2 Andy Long, 1 Soane Tonga'uiha.
Replacements: 16 Ross McMillan, 17 Alex Waller, 18 Paul Doran-Jones, 19 Teimana Harrison, 20 Ben Nutley, 21 Martin Roberts, 22 Ryan Lamb, 23 Tom May.
Referee: Andrew Small