Exeter moved into second position in their Amlin Challenge Cup Pool on Friday thanks to a clinical 34-19 victory over Bourgoin at Stade Pierre Rajon.
The Aviva Premiership newcomers bounced back from defeat in their opening tie to keep alive their hopes of progressing into the knockouts.
Tries from Bryan Rennie and Hayden Thomas gave the Chiefs a surprise 26-5 half-time lead at Stade Pierre Rajon before Mark Foster completed the historic win.
Bourgoin also scored three tries but the boot of Chiefs fly-half Gareth Steenson proved the difference with 19 points.
Exeter rang the changes for the visit to the former Challenge Cup champions, recalling a raft of front-line players following last week's defeat to Montpellier.
Steenson was back in the driving seat at fly-half and wasted no time in opening a six-point lead in as many minutes with two penalties.
Bourgoin number eight Yan Labrit rumbled over after nine minutes but Steenson hit back almost immediately with a third kick.
Centre Rennie crossed after 23 minutes to open breathing space before a moment of opportunism from Thomas saw Exeter take a grip on the game.
The scrum-half pounced when the ball squirted out of a Bourgoin scrum and galloped over from 30 metres out. Steenson converted and added a penalty before half-time.
Brando Va'aula spearheaded the anticipated backlash from the home side but wing Foster skipped over to safeguard's Exeter's lead.
Fit-again Richard Baxter marred his first start of the season following injury with a yellow card just moments after Ratu Nasiganiyavi was sent to the sin bin. The Fijian returned to score in the final minute but that was too late to deny Exeter.
Tries: Bougherara, Va'aulu, Nasiganiyavi
Con: Viazzo 2
Tries: Rennie, Thomas, Foster
Con: Steenson 2
Pen: Steenson 5
Bourgoin: 15 Mael Moinot, 14 Brando Va'aulu, 13 Matias Viazzo, 12 David Janin, 11 Ratu Nasiganiyavi, 10 Sebastien Laloo, 9 Mickaël Forest, 8 Yan Labrit, 7 Alex Tulou, 6 Timothy Cowley, 5 Camille Levast, 4 Thomas Genevois, 3 Stephane Bougherara, 2 Tone Alefa Kopelani, 1 Erwan Iapteff.
Replacements:16 Julien Janaudy, 17 Vincent Pelo, 18 Sylvain Charlet, 19 Albin Louchard, 20 Wessel Jooste, 21 Jérémy Gondrand, 22 Willem van Zyl, 23 Silvère Tian,
Exeter Chiefs: 15 Luke Arscott, 14 Andy Higgins, 13 Phil Dollman, 12 Bryan Rennie, 11 Mark Foster, 10 Gareth Steenson, 9 Haydn Thomas, 8 Richard Baxter, 7 James Scaysbrook, 6 Tom Johnson, 5 James Hanks, 4 Tom Hayes, 3 Chris Budgen, 2 Neil Clark, 1 Brett Sturgess.
Replacements:16 Chris Whitehead, 17 Ruaidhri Murphy, 18 Ignacio Elosu, 19 Dave Gannon, 20 Chad Slade, 21 Junior Poluleuligaga, 22 Garrick Cowley, 23 Nick Sestaret,
Referee: James Jones