The margin on the scoreboard looked slim at the finish, but in reality there was a gulf in class between Gregor Townsend's side and their English opponents. Glasgow will head into their RaboDirect PRO12 campaign with confidence soaring, taking a further boost from the fact that they will meet Exeter again in this season's Heineken Cup.
Exeter flattered themselves when Tom James, their Wales international centre, scored his second try in the last move of the match. Their blushes were also spared by the fact that Glasgow had turned down a number of kickable penalty chances earlier in the contest. But there was never any question that Glasgow were, by a distance, the better side.The best news for Warriors followers was that the quality of the performance was sustained even as replacements poured off the bench in the second half. Townsend has talked about wanting depth in his squad and his players demonstrated it brilliantly as they stepped into each other's roles seamlessly.
Chris Cusiter made a satisfying return after an 11-month absence with a shoulder injury but the real surprise package in the Glasgow ranks was Byron McGuigan, little more than an occasional utility player until now, who turned in a wonderfully clever display, embroidering his performance with two sharp tries.
Certainly, McGuigan's contribution has given Townsend much to think about ahead of Friday's season opener against Cardiff at Scotstoun.
"There were a lot of positive things out there," said Townsend. "Our defence was really aggressive and they kept to their systems most of the time. In attack, we played some good rugby when we held our depth."
As the coach also pointed out, there were errors as well, but most of those were caused by an excess of ambition. At times, Glasgow lost patience going forward and as mesmerising as some of their passing was, they got too loose on several occasions. It wasn't all carnival stuff, though, as they also dished out a few lessons at the breakdown. Glasgow played with speed and ferocity through contact, where Rob Harley made a conspicuous - sometimes too conspicuous - nuisance of himself. Chris Fusaro, another on the comeback trail after a long injury absence, also added to the overall effort.
McGuigan's first try arrived in the 19th minute. Things had been pretty even up to that point, Exeter leading 6-3 thanks to a couple of Gareth Steenson penalties to one by Scott Wight. However, Glasgow looked sharper with ball in hand and a sharp break by Alex Dunbar and a kick that bounced kindly gave McGuigan the space to score in the left corner.
His second came just before the interval, a lovely step inside taking him over. By the time James hit back with the first of his brace, in the 60th minute, Dunbar had collected Glasgow's third touchdown.
Mark Bennett scored the Warriors' fourth in the 72nd minute, a feat that was all the more impressive as it came just moments after he had all but chopped the unfortunately named Jason Shoemark in half with the best tackle of the game.