Despite dominating the game it took Glasgow until injury time to collect the bonus point when Donnie Macfadyen bagged their fourth try.
They had made a superb start but could only show three Calvin Howarth penalties for their early pressure, however with Connacht's Paul Warwick in the sin bin Glasgow took advantage of the extra man by sending Sean Lamont in at the corner with a huge miss-pass by Howarth.
They had a great chance to stretch their lead a minute after the restart, but
this time Howarth was wayward. He made quick amends, however, by embarking on the run which paved the way for Glasgow's second touchdown by Canadian World Cup prop Kevin Tkachuk - converted by Howarth.
Even better was to come for the Warriors when Lamont collected his second score following a great run by Colin Shaw. Howarth again added the extras.
Dan Parks added the conversion to Macfadyen's late try to complete the rout