Exeter ended Glasgow's unbeaten start to the season after they fought back to win a gripping European Champions Cup opener 24-15 at Sandy Park.
The Aviva Premiership champions had lost three of their previous four opening games in Europe, and they made a terrible start as Glasgow surged 10 points clear through a Tommy Seymour try, plus a Finn Russell conversion and penalty.
But the Chiefs, unbeaten at home in all competitions since last December, wiped out the deficit when prop Harry Williams and lock Jonny Hill claimed tries during a dominant nine-minute spell, with fly-half Gareth Steenson converting both scores.
And Glasgow, who lost Scotland international hooker Fraser Brown to injury early in the action, were ultimately defeated despite wing Lee Jones' 44th-minute touchdown.
A Steenson penalty and number eight Sam Simmonds' late converted touchdown saw Exeter home.
It was Glasgow's first defeat following six successive Guinness PRO14 wins, yet they could still feature heavily in the Pool Three mix.
A fearsome group also includes three-time European champions Leinster and French heavyweights Montpellier, suggesting it is likely to go down to the wire in January when quarter-final places are decided.
Exeter head to Montpellier next weekend, while Glasgow host Leinster, and the Chiefs are off and running in Europe following an absorbing encounter high in intensity and intent.
Injured England wing Jack Nowell was replaced in the Chiefs side by Lachie Turner, with Phil Dollman returning at full-back, while flanker Julian Salvi also started after Dave Dennis missed out due to an injury suffered during training.
Glasgow showed two changes to their starting line-up following last weekend's victory over the Cheetahs in Bloemfontein, with wing Jones and centre Peter Horne both returning as the Warriors put their unbeaten record on the line.
Russell made amends for putting the kick-off straight into touch by booting a sixth-minute penalty, but Glasgow then suffered a major blow when Brown departed with what appeared to be a knee injury.
Scotland head coach Gregor Townsend looked on as Brown gingerly left the action four weeks before the autumn series opener against Samoa.
Glasgow were not knocked out of their stride and they went further ahead when Russell's cross-kick saw Seymour easily out-jump Dollman to claim a try that Russell converted.
It was an outstanding start by the Warriors, but Exeter then stirred through their forwards, putting together a number of phases inside Glasgow's 22, and pressure eventually told as Williams touched down from close range and Steenson added the extras.
And the Exeter pack had no intention of leaving matters there, as further sustained pressure ended with another impressive show of power that ended with Hill claiming a try that Steenson converted for a 14-10 advantage after 27 minutes.
Steenson kicked a penalty early in the second half, but Glasgow responded after Exeter scrum-half Nic White fumbled possession near his line, then lost the ball completely as Russell tackled him, and Jones capitalised to post Warriors' second try.
It set up a tense final quarter, with Glasgow well and truly back in the contest and Exeter having to display all of their trademark efficiency and organisation to stay in front.
Steenson saw a penalty that might have sealed the deal hit a post nine minutes from time, yet Exeter had just enough in the tank to finish on top.