Tom Jordan's try gave Glasgow the lead at half-time

Scores from debutant Kyle Rowe, Tom Jordan, Jamie Dobie and a penalty try gave Warriors the try bonus but they were not able to build on their 43-25 home win over Leinster last weekend.

The visitors could have taken so much more from the game but Connacht were able to exploit Glasgow's poor discipline to kick give penalties.

Warriors went into the break 19-14 ahead but Connacht dominated after the restart although they weren't able to grab a bonus point.

Warriors kept battling and secured a bonus point when Jamie Dobie got over in the closing stages after a patient build-up.

"I think we went something like 30 phases to get that bonus point try at the end," said Glasgow head coach Franco Smith. "The equipment is there, experience is something you have got to experience. It's not something I can tell them. I knew it would take a special effort to come and beat Connacht here.

"A lot of teams are going to come here and lose, so I'm not that concerned about the loss. I think there are things that we can adjust and do better and that's part of the growth of the group."