Rufus McLean went over for two tries

Glasgow tries came from Rufus McLean (2), Kyle Steyn (2), Fraser Brown and Johnny Matthews with Duncan Weir kicking the other points.

Tries for Connacht from Sammy Arnold and Paul Boyle along with kicks by Cathal Forde made it a close-run game before Warriors stretched away in the final quarter to claim the win.

The Sportsground is always a tough place for visiting teams but Warriors started brightly and, after good work from forwards and backs, Scotland winger McLean went over in the left corner, via a George Horne pass.

Glasgow's early momentum was lost when Richie Gray was binned for an illegal clear-out on Ultan Dillane.

A fine 50:22 kick from Tiernan O'Halloran, put Connacht into Glasgow territory and Forde's short pass sent Arnold over.

Warriors ended the opening quarter with a 12-7 lead, Steyn shrugging off a struggling Tom Farrell's attempted tackle to score after nice work from Sione Tuipulotu.

With five minutes left before the break Warriors went to the corner with a kickable penalty and impressive maul work sent Brown over for a try.

Careless play from Warriors let Forde sneak in a late penalty to close the gap to seven points at the interval

Connacht made a quick fire start to the second period and Boyle burrowed over for Forde to kick Connacht level.

Weir and Ford exchanged penalties before Boyle's binning for going off his feet had the hosts under pressure. Glasgow pressure eventually told when Weir looped a pass out for McLean to notch the bonus point in the corner.

Weir then converted Steyn's second score, the South African-born centre capitalising on a partially-blocked kick.

With Connacht tiring Weir kicked a penalty to end any home hopes but there was still time for Matthews to go over after another well-executed Glasgow maul.

Glasgow Head Coach Danny Wilson was satisfied with his team's display.

"I know they were missing a few internationals but we were missing seven," said Wilson. "I thought we controlled the game well. We attacked well, our set-piece was good and we put a lot of pressure on their lineout.

"We knew it was going to be tough coming here and it was pretty stalemate for quite a long time but I thought we controlled the game in terms of what the boys executed tactically."