Paul Diggin scored a late try for Northampton Saints to secure a 15-18 Aviva Premiership Rugby victory at Sandy Park moving the Saints back into the top four.
Northampton were leading 10-11 as the match drew to a close but then Paul Diggin scored the decisive try which Stephen Myler converted to give the Saints an 8 point lead.
Exeter scored as well at the death but Richard Baxter's try turned out to be a consolation try.
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.
Final Score Exeter 10 (10) Northampton 18 (3)
Tries: Camacho, Baxter
Tries: Ashton, Diggin
Penalties: Myler 2
15 Phil Dollman , 14 Gonzalo Camacho , 13 Bryan Rennie , 12 Jason Shoemark , 11 Matt Jess , 10 Ignacio Mieres , 9 Haydn Thomas , 1 Ben Moon , 2 Chris Whitehead , 3 Hoani Tui , 4 Tom Hayes (capt) , 5 James Hanks , 6 Tom Johnson , 7 James Scaysbrook , 8 Richard Baxter
16 Neil Clark , 17 Brett Sturgess , 18 Chris Budgen , 19 Aly Muldowney , 20 Ben White , 21 Kevin Barrett , 22 Gareth Steenson , 23 Sireli Naqelevuki
15 Ben Foden , 14 Chris Ashton , 13 George Pisi , 12 James Downey , 11 Paul Diggin , 10 Stephen Myler , 9 Lee Dickson (capt) , 1 Soane Tonga’Uiha , 2 Andy Long , 3 Brian Mujati , 4 Mark Sorenson , 5 Christian Day , 6 James Craig , 7 Phil Dowson , 8 Roger WILSON
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,