Glasgow (8) 30
Tries: Shaw, O'Hare (2), Low Con: Gregor (2) Pens: Gregor (2)
Connacht (9) 9
Pens: Keatley (3)
Glasgow made hard work of their bonus-point win at Firhill
Glasgow left it late to turn on the style and secure a bonus-point victory in a scrappy close to the season at a rain-soaked Firhill.
The visitors, a distant last in the Magners League, led 9-8 at half time thanks to the kicking of Ian Keatley.
However, Hefin O'Hare plunged over twice and Moray Low also added to Colin Shaw's fine first half touchdown.
Colin Gregor kicked the rest of the home team's points but it was a sloppy, error-strewn display all round.
The best Glasgow can hope for is a seventh place finish in the table and that will frustrate head coach Sean Lineen after a promising start to the campaign.
An injury-hit Glasgow side held the upper hand during the jittery opening period but they were unable to turn their superiority into a significant points advantage.
Gregor edged them in front with a penalty from close range, only for Keatley to reply from 45 metres .
Warriors surged ahead again with their first fluent attack with a fine try by Shaw.
Connacht's problems began when full-back Troy Nathan was yellow carded for deliberately palming a Graeme Morrison chip into touch.
From the set piece, Glasgow swung the ball across the field to Lome Fa'atau, whose grubber kick was perfectly weighted for Shaw to pounce.
The hosts continued to look the more potent outfit but their good work was spoiled by giving away a spate of penalties in their own half.
And Keatley punished them again by landing two more kicks between the posts before the interval.
A Keatley penalty drifted wide early in the second half and Gregor defied the elements to thump over a difficult kick at the other end.
But the scrum-half then squandered a much easier chance.
A previously dreadful contest was suddenly lit up midway through the half thanks to some inspired play from O'Hare.
The centre marked the extension of his Glasgow contract by swerving past four opponents before squeezing over for a remarkable touchdown.
Low then ploughed through for the third try, goaled by Gregor.
He added another when O'Hare again left the Connacht defence for dead to put a flattering complexion on the Glasgow tally.
Glasgow: Stortoni, Faatau, O'Hare, Morrison, Shaw, Jackson, Gregor, Tckachuk, McArthur, Low, Gray, Kellock, Eddie, Brown, Forrester.
Replacements: Horne for Morrison (79), Nunez Piossek for Shaw (78), McMillan for Jackson (40), Milligan for McArthur (73), Welsh for Low (79), Turner for Kellock (59), Swindall for Eddie (68).
Connacht: Nathan, Carr, Duffy, Matthews, Bibo, Keatley, Murphy, Wilkinson, Flavin, Loughney, Swift, Farley, Browne, Ofisa, J. Muldoon, Rigney.
Replacements: Rigney for Carr (49), O'Loughlin for Murphy (66), Higgins for Loughney (50), Gannon for J. Muldoon (73), Deane for Rigney (73). Not Used: Cronin, Dunne.
Ref: Nigel Owen (WRFU).