|Connacht (6) 13|
|Tries: Muldowney Cons: Carty Pens: Carty 2|
|Glasgow (19) 31|
|Tries: Matawalu 2, Hogg, Ashe, Seymour Con: Russell 3|
Glasgow moved back to the top of the Pro12 table as they dented Connacht's European qualification hopes in Galway.
Two Jack Carty penalties put Connacht 6-0 ahead but two Niko Matawalu tries and a Stuart Hogg score helped the visitors lead 19-6 at the interval.
An Aly Muldowney try helped Connacht cut the lead to 19-13 but Carty's third penalty miss hindered the home side.
Adam Ashe's 68th-minute score secured Glasgow's bonus point before Tommy Seymour added a fifth Warriors try.
Glasgow's win moves them three points ahead of Ulster who briefly went top of the table after Friday's 26-10 victory over champions Leinster while Connacht are now out of the top six after Edinburgh's win over Zebre.
Connacht need to finish in the top six to clinch a place in next season's European Champions Cup.
The Irish province produced all the early pressure with a series of forward drives yielding two successful penalties for fly-half Carty.
However, Connacht's early promise then began to be undermined by a series of set-piece errors.
After a line-out over-throw from Tom McCartney, the home side were then punished following a botched scrum as Fijian Matawalu ran in his first try after a brilliant one-handed off-load from Fraser Brown.
Following Finn Russell's conversion miss, Carty had two glorious penalty chances to extend but was badly off-target.
Connacht's failure to put more points on the board was emphasised when the Scots stung them with two opportunist tries in the three minutes before half-time.
A series of missed tackles allowed Seymour to sail through midfield and his pass put Hogg over to the right of the posts.
Russell converted and also added the extras to Glasgow's third touchdown which saw Matawalu intercept Henshaw's attempted pass as Connacht tried to counter from deep in injury-time.
Seymour's 47th-minute sin-binning for a ruck offence gave Connacht the chance to produce pressure and a series of attacks eventually yielded Muldowney's try as he reached to score.
Carty's conversion cut the margin to 19-13 but his horrible penalty miss from in front of the posts on the hour seemed to knock the stuffing out of Connacht.
Despite having flanker Chris Fusaro in the sin-bin, Glasgow secured the bonus point on 68 minutes as replacement Josh Strauss's break set up a simple finish for Ashe.
Glasgow's clinical display was wrapped up five minutes later as Seymour scored in the corner after some slick passing.
Connacht: Tiernan O'Halloran, Danie Poolman, Robbie Henshaw, Bundee Aki, Matt Healy, Jack Carty, Kieran Marmion; Denis Buckley, Tom McCartney, Rodney Ah You, Ultan Dillane, Aly Muldowney, John Muldoon (capt), Eoghan Masterson, Eoin McKeon.
Replacements: Ronan Loughney for Buckley 68, Finlay Bealham for Ah You 68, Andrew Browne for Dillane 52, George Naoupu for Masterson 62, John Cooney for Marmion 49 mins, Miah Nikora for Carty 62, Darragh Leader for Henshaw 53.
Not used: Shane Delahunt
Glasgow Warriors: Stuart Hogg, Tommy Seymour, Richie Vernon, Peter Horne, Niko Matawalu, Finn Russell, Henry Pyrgos; Jerry Yanuyanutawa, Fraser Brown, Euan Murray, Leone Nakarawa, Jonny Gray (capt), Rob Harley, Chris Fusaro, Adam Ashe.
Replacements: Kevin Bryce for Brown 51, Ryan Grant for Yanuyanutawa 41, Jon Welsh for Murray 41, Tim Swinson for Nakarawa 53, Josh Strauss for Harley 53, Duncan Weir for Russell 68, Peter Murchie for Strauss 72, Lee Jones for Matawalu 70.
Referee: Marius Mitrea (FIR)
Assistant referees: Andy Brace, Oisin Quinn (both IRFU)
Citing commissioner: Dennis Templeton (IRFU)
TMO: Dermot Moloney (IRFU)