However, Sean Lineen's men were far from convincing in sealing a tense triumph against a dogged Irish outfit at their new Maryhill home.

Glasgow struggled to settle as a string of unforced errors gave Connacht the early initiative.

In just four minutes Tim Donnelly slotted a penalty after the home forwards strayed offside.

Gregor did get Glasgow off the mark with a 40-metre kick from in front of the posts and the Warriors were handed a further boost when Colm Rigney was sin-binned for an off-the-ball tackle.

And the Scottish side suddenly shifted up a gear in a bid to make the extra man count.

Kiwi Daryl Gibson was first to inspire Glasgow with a surging run from his own half.

Then Bernardo Stortoni linked neatly with Gibson to release Max Evans whose searing pace took him deep into the Connacht 22. However, Sam Pinder denied by Mel Deane's desperate last-ditch tackle.

Glasgow refused to be denied and the next phase resulted in a scrum five from which Stortoni deceived the Irish defence with a deft side-foot before Johnny Beattie plunged over.

Gregor added the conversion as the Warriors took control.

They almost notched a second try within a few minutes when a switch pass by Evans found Stortoni racing through again. However, the flying Argentinian's wayward pass failed to find Pinder who had looked certain to score.

Stortoni was in the thick of it again with another dangerous break on the right flank and only resolute Irish tackling kept him out.

Glasgow were left to rue their failure to cash in on a spell of dominance when Donnelly reduced the deficit with a drop-goal on the stroke of half-time.

But Gregor restored the seven-point advantage with his second penalty after Moray Low's burst had forced an infringement.

Donnelly responded with a further kick before Gregor looked certain to score after Stevie Swindall and Low combined to send the scrum-half darting towards the line.

However, Ofisa Treviranus produced a try-saving tackle to knock the ball from the Glasgow player's grasp.

The deficit was reduced to a single point when Donnelly landed his second drop goal of the night with a superb 45-metre effort.

Gregor failed to ease the nerves when he missed his third penalty of the match and instead Donnelly put the visitors ahead with a monster penalty from the halfway line.

Gregor atoned for earlier errors with an easy kick in the 80th minute but the home side still had to survive 10 anxious minutes of stoppage time before clinching their first win.

Glasgow Warriors 10 (16)
Tries: Beattie
Cons: Gregor
Pens: Gregor 3.

Connacht (6) 15
Drop goals: Donnelly 2
Pens: Donnelly 3.

Glasgow: Stortoni, M. Evans, Morrison, Gibson, Shaw, Gregor, Pinder, Kalman, Milligan, M. Low, Newman, Kellock, Swindall, Eddie, Beattie.

Replacements: O'Hare for Shaw (51), Prescott for Kalman (70), McArthur for Milligan (68). Subs not used: Turner, Vernon, Forrester, Barrow.

Connacht: Durcan, Treviranus, Deane, Wynne, Matthews, Donnelly, McPhillips, Wilkinson, Flavin, Loughney, Swift, Gannon, McCarthy, J. O'Connor, Rigney.

Replacements: O'Loughlin for McPhillips (74), Fogarty for Flavin (70), Morris for Loughney (3), Ofisa for McCarthy (51), J. Muldoon for Rigney (51). Subs not used: Riordan, Tuilevuka.