Glasgow secured their first win over Connacht in five games with a 24-3 win in front of a home crowd at Firhill.
The prize for Glasgow was a place in the play-offs and a semi-final clash against Leinster at the RDS, whereas Connacht were simply playing for pride.
Even so, visiting coach Eric Elwood believed that he could add to his string of good results over Glasgow. He said: "We've got mixed emotions. We came here to win and perhaps did not play as well as we might have. But to finish eighth with this bunch of players is still a great achievement.
"We've made an improvement from last year when we finished ninth. So again it's another step up. It's Connacht's best season in the Rabo."
At the end of a tight first half Connacht were still in touch, trailing 11-3.
Two penalties by Glasgow out-half Duncan Weir to one by his opposite number Miah Nikora had the hosts just ahead.
Nikora's kick, however, was to be his side's only score of the match as Glasgow gradually took a grip of the game, scoring a try early in the second quarter through Canada wing DTH van der Merwe.
In the second half, Weir added two more penalties before the Warriors, taking advantage of the sin-binning of replacement scrum-half Paul O'Donohoe, delivered the coup de grace with a pushover try credited to No 8 John Barclay.