Wobbly Glasgow Warriors restored some pride to Scottish rugby but they almost made a hash of snuffing out the challenge of the Pro12 basement boys at Scotstoun.
A spate of missed penalties by Ruaridh Jackson and a series of wasted try chances threatened to dent their play-off qualification hopes.
But they managed to survive to get the important win, though they couldn’t claim a precious bonus point.
The early action was predictably scrappy on a greasy surface.
Glasgow had a reprieve in the third minute as Craig Ronaldson sent his penalty attempt wide.
Home centre Mark Bennett then burst into the contest to set up the first clear-cut try chance.
He looked destined to reach his own chip into the danger zone, only for the ball to dribble out of play at the last gasp.
Connacht replied in positive style as Ronaldson made amends with his next strike.
Warriors then launched a potent looking raid through Niko Matawalu, but it all fizzled out thanks to determined marking by the Irishmen.
But it was Bennett who was in the right place at the right time to get Glasgow off the mark, using his impressive pace to get the first touch to a through ball from scrum half Henry Pyrgos for a great try.
Jackson was off-target with the conversion bid with Ronaldson also failing with two penalties in quick succession at the other end.
The huge Connacht pack stepped up the pressure in the approach to the interval, but somehow the hosts staved them off and grabbed a crucial turnover to preserve their lead.
However, Ronaldson edged the visitors in front with a simple penalty in stoppage time.
Warriors looked more urgent after the restart and Jackson gave them an instant boost by reclaiming the two point edge.
Then new loan signing Lee Jones set up another chance with a powerful run deep into enemy territory, but it came to nothing.
Another huge cheer rang out on the hour-mark when former Scotland and Warriors hero Dan Parks came off the bench for the visitors.
Glasgow continued to create opportunities, but still their finishing was less than clinical. And the nerves began to jangle when Jackson missed his next two goal attempts going into the final stages.
He was handed yet another chance two minutes from time but his luck was out as the ball crashed against the bar and rebounded to safety.
* Leinster moved to within three points of RaboDirect PRO12 leaders Munster with a 31-8 win at Zebre.