|European Champions Cup|
|Glasgow Warriors (7) 28|
|Tries: Hogg, Penalty, Seymour, M Fagerson Cons: Russell 3, Penalty|
|Exeter (7) 21|
|Tries: Simmonds, Armand, Whitten Cons: Steenson 3|
Scotland full-back Stuart Hogg made a try-scoring comeback as Glasgow ensured Exeter's pursuit of a Champions Cup quarter-final place came up short.
Hogg crossed within two minutes, before Sam Simmonds' try brought Chiefs level at half-time.
Warriors took control with a penalty try and length-of-the-field scores from Tommy Seymour and Matt Fagerson.
Exeter refused to give up, tries from Don Armand and Ian Whitten bringing them to within a score.
But a losing bonus point was not enough to preserve the English champions' hopes of securing one of the three best runners-up spots.
For Glasgow, it was a first win from an otherwise bleak European campaign, but they lost two Scotland players - George Turner and Alex Dunbar - to first-half knee and head injuries respectively.
There was also a worrying sight for England coach Eddie Jones with centre Henry Slade forced off in the second half clutching his shoulder, with the Six Nations a fortnight away.
This was an exercise in pride restoration for Glasgow, claiming the scalp of the English champions at the end of a bleak European journey.
Their hunger in defence, augmented by the intelligent kicking of Finn Russell and telling touches from the imperious Hogg were vital tenets of a continental triumph that has eluded them all season.
The first half was played almost exclusively in the home half, but began with a flourish of brilliance from the Warriors backs.
Russell carved open the Chiefs midfield and flipped inside to George Horne, running a razor-sharp support line. The scrum-half had Hogg screaming for the pass with a clear run under the posts, Russell converting.
From that point on, it was rearguard stuff for Glasgow, Exeter probing and bludgeoning, testing Warriors' fringe defence where it had crumbled in the corresponding fixture at Sandy Park.
On one flank, Olly Woodburn was hunted down by Seymour as he hared towards the whitewash. On the other, Leo Sarto hauled Lachie Turner to the deck by his ankles with the line beckoning.
This unrelenting defensive toil took its toll. Off limped Turner and Dunbar with injuries that could have implications for their Six Nations prospects. Adam Ashe required a head injury assessment he passed, and Matt Smith became another first-half casualty.
For all their stubbornness, Warriors looked to have committed an act of grievous self-harm when the they lost ball out of a scrum in their own 22, and the Chiefs sent Whitten sprinting for the line. Huw Jones - after being swatted aside initially - scrambled back to stop Whitten grounding the ball.
But the Chiefs eventually got there in the final minute of the half, Simmonds driving over from a couple of yards and Gareth Steenson converting to level the half-time scores.
Exeter were dealt a seismic blow 12 minutes into the second period. With Glasgow players queuing up to score down the blind side, Nic White was sin-binned for slapping Russell's pass forward in the tackle.
Referee Romain Poite brandished his yellow card, before jogging under the posts to award Warriors a penalty try.
Glasgow then conjured two utterly mesmeric scores in two scintillating minutes. Hogg was the fulcrum for both, the sorcerer revelling on his return from a two-month injury lay-off.
First he took Russell's pass and seared up the right touchline, before lofting a pass inside to Horne. The scrum-half jinked and slalomed to within a few yards of the line, before popping on to Seymour for the try.
Then Hogg arced through the Chiefs midfield, Seymour and Horne involved again before Fagerson crashed over.
Russell converted both, but Exeter were not dead yet.
The contest became blisteringly fast and loose, high-octane flair replacing the monotonous drudgery of the first half.
Armand drove over, then Whitten finished a sumptuous counter-attack in the corner, Steenson booting the extras to bring Chiefs to within seven points.
Needing to score at least one try for a second bonus point, and twice to win, they huffed and puffed, but squandered what ball they had.
A European victory for Glasgow at last, a raucous afternoon at Scotstoun, but a lingering pang of what might have been had they found this calibre of display earlier in the campaign.
Glasgow: S Hogg, T Seymour, H Jones, A Dunbar, Leonardo Sarto, F Russell, G Horne; J Bhatti, G Turner, S Halanukonuka, R Harley, J Gray (capt), M Fagerson, M Smith, A Ashe.
Replacements: G Stewart (for Turner, 8), A Allan (for Bhatti), D Rae, G Peterson (for Ashe, 72), C Fusaro (for Smith, temp, 30), A Price (for G Horne, 70), P Horne (for Dunbar, 12), L Jones.
Exeter: P Dollman; L Turner, H Slade, I Whitten, O Woodburn; G Steenson (capt), N White; B Moon, L Cowan-Dickie, H Williams, M Lees, J Hill, D Ewers, D Armand, S Simmonds.
Replacements: E Taione, M Low, T Francis, T Salmon, M Kvesic, W Chudley, J Simmonds, T Gilbert-Hendrickson.