Glasgow 19-30 Connacht
Glasgow (5) 19
Tries: Morrison, Harrison, Beardshaw
Cons: Parks 2
Connacht (23) 30
Tries: McPhillips, Walls, Mostyn
Cons: McHugh 3
Pens: McHugh 3
Glasgow hurtled to earth with a bump at Hughenden as dark horses Connacht completed their dream treble over Scotland's pro teams this season.
The home side's hopes had been high in the wake of their Celtic Cup triumph at Bridgend, but they fell to pieces against the spirited Irishmen.
Honours were even in the scrappy opening sparring session, though Glasgow wasted a great opportunity to make an instant impression.
Full-back Stuart Moffat had wing Gareth Maclure unmarked on his outside but opted to go on his own and was hauled down as he dashed into the 22 zone.
Calvin Howarth was then handed a chance to break the deadlock with a penalty following fine work by Maclure, Moffat and Jon Steel, but he was off-target.
Howarth squandered an even easier penalty opportunity and the Irish province made the most of their reprieve by edging in front with a long-range angled effort by Mark McHugh.
Moffat was soon back in attack to help create Joe Beardshaw's first try for Glasgow.
But, yet again, Howarth was wide with the kick.
Even worse was to come for Glasgow as scrum-half Mike Walls darted through for a fine opportunist score, converted by McHugh.
Connacht grabbed total control with a further burst of points before the break.
Lee Harrison scored one of Glasgow's consolation tries
McHugh banged over two more penalties and converted a try by substitute wing Matt Mostyn to leave the home side in trouble.
Their third try was claimed by wing Conor McPhillips, with McHugh completing his conversion hat-trick.
Glasgow eventually broke through with a score by Graeme Morrison and a Lee Harrison effort, converted by substitute Dan Parks.
But the home side were never really in the hunt as Connacht took the points.
Glasgow: S. Moffat, Steel, Morrison, A. Bulloch, MacLure, Howarth, McMillian, A. Kelly, Gunn, Harrison, Hall, Beardshaw, Mather, MacFadyen, Reid.
Replacements: Lawson, Murray, Ross, Dearlove, Sinclair, Parks, Millard.
Connacht: McHugh, McPhillips, Yapp, T. Allnut, Munn, Hewitt, Walls., Hogan, Jackman, Boiroux, Browne, Farley, Swift, Neville, O'Sullivan.
Replacements: Fogarty, Howell, McCarthy, Carter., Keane, Moore, Mostyn.
Referee: Nigel Owens (Wales)