Stade Franšais edged Exeter 22-17 thanks to a 79th-minute try to centre Paul Williams in Thursday's Amlin Challenge Cup quarter-final.
With the teams tied at 17-17 late in the match and extra-time beckoning, a break by scrum-half Julien Dupuy led to Williams crossing over for the decisive try to shatter the visitors' hopes at Stade Charlety in Paris.
The last-gasp victory puts the French club into this season's Amlin Challenge Cup semi-finals where they will face an away tie against either Toulon or Harlequins on April 27.
Stade Franšais, last year's losing finalists, ultimately proved too strong for a plucky Exeter side despite failing to dominate the game.
Chiefs fly-half Ignacio Mieres opened the scoring with a 20th minute penalty after the home side strayed offside at a ruck.
The Argentinian missed his second effort but then saw counterpart and compatriot Felipe Contepomi sin-binned soon after for reacting to a bone-crunching hit by hooker Chris Whitehead with a wild, swinging punch.
Mieres kicked the ensuing penalty, but Dupuy clawed one back for the home side after a reckless tackle by Exeter winger Gonzalo Camacho.
The respective kickers then traded penalties to leave the half-time score at 9-6 and the game delicately poised with each team failing to find their rhythm.
Stade Franšais came out firing on all cylinders in the second period, a dink through from Contepomi eluding the covering Phil Dollman but falling nicely for Djibril Camara, the full-back stretching to dot down in the corner for the game's first try.
Dupuy missed the conversion but hit a penalty in the 48th minute, cancelled out immediately by Mieres.
The France halfback was on target again to stretch Stade's lead to 17-12.
But with 11 mintues remaining, missed tackles from Contepomi and Dupuy allowed Exeter's Fijian centre Sireli Naqelevuki in for a soft try, Mieres missing the conversion to leave the scores tied.
The Argentinian, a former Stade Franšais player, then crucially missed a snatched drop-goal. The Parisians came roaring back up the pitch and Dupuy found a gap and sent out an inch-perfect pass to the fast-approaching Williams for the match-winner.
For Stade Franšais:
Tries: Camara, Williams
Pens: Dupuy 4
For Exeter Chiefs:
Pens: Mieres 4
Stade Franšais: 15 Djibril Camara, 14 Paul Sackey, 13 Morgan Turinui, 12 Paul Williams, 11 Julien Arias, 10 Felipe Contepomi, 9 Julien Dupuy, 8 Sergio Parisse, 7 Antoine Burban, 6 George Smith, 5 Pascal Pape, 4 Anton van Zyl, 3 Rabah Slimani, 2 Dimitri Szarzewski, 1 Rodrigo Roncero.
Replacements: 16 Laurent Sempere, 17 Olivier Milloud, 18 Stan Wright, 19 Alexandre Flanquart, 20 David Lyons, 21 Pierre Rabadan, 22 Jerome Fillol, 23 Hugo Bonneval.
Exeter Chiefs: 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 (c), 3 Craig Mitchell, 2 Chris Whitehead, 1 Hoani Tui.
Replacements: 16 Neil Clark, 17 Ben Moon, 18 Chris Budgen, 19 Aly Muldowney, 20 Ben White, 21 Kevin Barrett, 22 Gareth Steenson, 23 Sireli Naqelevuki.