Gordon Reid's try levelled the score just after the break

For the last 30 minutes Warriors played with 14 men after prop Sila Puafisi was sent off and they know they can't afford similar indiscipline when they return in a fortnight.

Pat Lam's men will hope for a repeat result as they strive to reach their first ever final at the end of what is already the Irish province's best ever league campaign.

Bundee Aki's 17th-minute try gave the hosts a 7-0 half-time lead, with Finn Russell missing two kickable penalties for Glasgow.

Gordon Reid's well-taken try tied things up, but his front row colleague Puafisi was sent off in the 49th minute for a dangerous head first challenge on Kieran Marmion.

Replacement Shane O'Leary provided the assist and conversion for Tiernan O'Halloran's vital 59th-minute touchdown, and the hosts saw out the hard-fought victory with some defiant late defence.

Russell sent an early penalty wide after Leone Nakarawa had slipped clean through from a ruck to launch Glasgow's first attack from deep.

A nervy Russell also overcooked a touch finder, but Nakarawa soon broke the line again, stretching the home defence until prop Reid knocked on in the 22.

But Connacht were clinical from their very first attack, Marmion and AJ MacGinty linking smartly off a close range maul before Aki used his power to make it over by the right hand post. MacGinty converted for 7-0.

A scrum penalty was nudged wide by Russell and with Sean O'Brien and Ultan Dillane leading a resolute Connacht defence, the Warriors remained scoreless.

Aki, who continued to threaten off limited ball, was a pass away from putting Robbie Henshaw over, and their captain John Muldoon was also denied just a metre out.

The home side were unable to profit from a snappy break by Marmion, the Ireland scrum half hardly putting a foot wrong on his 100th appearance for Connacht.

However, the Warriors were level within seven minutes of the restart. They won a series of penalties and prop Reid managed to crash over off the back of a close-in ruck. Russell's extras made it 7-7.

Connacht quickly got back into scoring range, though, and as tempers flared, input from TMO Olly Hodges saw referee Ian Davies dismiss Puafisi for leading with the head on Marmion at a ruck.

The home side, who had to move Tom McCartney to loosehead in a patched-up front row, should have scored from Marmion's blindside burst off a scrum and flanker O'Brien was also thwarted near the posts.

The breakthrough finally came when full-back O'Halloran rose above his opposite number Stuart Hogg to collect O'Leary's cross-field kick and dot down wide on the right.

The conversion was added by O'Leary before a smashing break by Simone Favaro and kick ahead almost put Hogg in for a quick response.

Some superb handling had Glasgow hammering on the door again with five minutes left, but Connacht forced another error and a final ruck penalty was enough to see them home.