Exeter remarkably advanced to the Champions Cup quarter-finals after scoring five tries to defeat the Ospreys 33-17.
Two tries in the first 10 minutes from Kai Horstmann and Thomas Waldrom sandwiched Hanno Dirksen's effort in a pulsating opening.
James Short scored two after the break to seemingly finish the game, but a penalty try did ensure Ospreys did have some hope at the end.
But a late try from Waldrom ensured Exeter will progress in dramatic style.
Needing a victory to top Pool 2 and progress, Ospreys made the worst possible start at Sandy Park, as they conceded a try within the opening three minutes.
After a quick tap and go, the ball came to Horstmann, who went over for the opening score. Gareth Steenson added the extra two, as Chiefs took charge in the opening exchanges.
But that dream start was quickly halted, when Ospreys went over for the second try of the game just four minutes later.
Dirksen forced his way over the line, after the visitors set up camp straight from the restart. Dan Biggar levelled with the conversion.
But Exeter hit back in what was a thrilling first 10 minutes, and Waldrom scored try number three. Again it came from the restart, and after Chiefs had knocked at the door, Waldrom let himself in after originally being held up a metre from the line. Steenson made no mistake, restoring the seven-point gap.
And after that hectic start, the next half hour didn't muster a single point. A number of injuries and substitutions broke down the momentum built up from the opening 10 minutes, though Chiefs did spend considerable time trying to extend their lead.
Ospreys' defence held firm though, and the sides went into the break two tries to one.
The visiting side started the second period strongly, and forced a penalty which Biggar slotted through. And just when it looked like the Welsh side were beginning to turn the screw, Scott Baldwin found himself sent to the sin-bin. It came after a challenge on Waldrom, coming late and giving the referee little option.
That yellow soon brought about another opportunity for the hosts, and they took it. Steenson's clever chip ball forward was collected by Short, and had the whole pitch ahead of him to breeze forward and finish try number three. Steenson couldn't find the posts, though the lead was still a healthy one.
Biggar almost reduced it immediately but his penalty from half-way fell agonisingly short. And with 15 minutes to go, Short was celebrating again, sealing the tie in the process.
After kicking for touch, possession was stolen by the Chiefs, and Waldrom's initial break saw him feed Short, who made no mistake on the way to the line. Steenson converted again, and a 16-point lead looked uncatchable.
But the visitors gave it a shot, and wiped out that try with one of their own. Pushing for the line, the Chiefs were forced to come in at the side of a driving maul, allowing the referee to award a penalty try that just made the game a little nervy for home supporters. Biggar reduced the lead to nine.
However with minutes to go, Exeter sealed victory with try number five. Waldrom powered over, eliminating Ospreys in the process, with Will Hooley finishing the scoring.
The Chiefs will now face off against Wasps for a semi-final place.
Tries: Horstmann, Waldrom 2, Short 2
Cons: Steenson 3, Hooley
Tries: Dirksen, Penalty Try
Cons: Biggar 2
Yellow Card: Baldwin
Exeter Chiefs: 15 Phil Dollman, 14 Olly Woodburn, 13 Michele Campagnaro, 12 Ian Whitten, 11 James Short, 10 Gareth Steenson, 9 Dave Lewis, 8 Tom Waldrom, 7 Don Armand, 6 Kai Horstmann, 5 Geoff Parling, 4 Jonny Hill, 3 Alex Brown, 2 Jack Yeandle, 1 Alec Hepburn
Replacements: 16 Elvis Taione, 17 Ben Moon, 18 Harry Williams, 19 Ollie Atkins, 20 Tom Johnson, 21 Haydn Thomas, 22 Will Hooley, 23 Max Bodilly
Ospreys: 15 Daniel Evans, 14 Hanno Dirksen, 13 Jonathan Spratt, 12 Josh Matavesi, 11 Eli Walker, 10 Dan Biggar, 9 Brendon Leonard, 8 James King, 7 Justin Tipuric, 6 Sam Underhill, 5 Alun-Wyn Jones (c), 4 Lloyd Ashley, 3 Dmitri Arhip, 2 Scott Baldwin, 1 Paul James
Replacements: 16 Sam Parry, 17 Nicky Smith, 18 Aaron Jarvis, 19 Rory Thornton, 20 Dan Baker, 21 Thomas Habberfield, 22 Sam Davies , 23 Owen Watkin
Referee: Jérôme Garcès (France)
Assistant Referees: Salem Attalah (France), Pierre Brousset (France)
TMO: Hervé Dubes (France)