Glasgow gave themselves a huge confidence boost ahead of next week's European Champions Cup quarter-final against Saracens by seeing off Connacht at Scotstoun.
Home lock Tim Swinson was shown a red card after 65 minutes for an incident at a ruck, but Glasgow still managed to secure a 35-24 victory in the Guinness PRO12 clash.
It allows the sixth-placed Scots to pull clear of Connacht, the team directly behind them, and lifts their hopes of squeezing into the top four.
And eight days before the clash with Saracens at Allianz Park, the sight of Sean Lamont galloping in from 30 metres to touch down for a bonus-point try late on capped a successful encounter.
For Connacht, the defeat hits their prospects of making a late run to earn a place in next season's Champions Cup.
The visitors had led 15-13 at the break, thanks to tries from Niyi Adeolokun and John Muldoon, plus a conversion and a penalty from Craig Ronaldson. Glasgow replied with Corey Flynn dotting down and Finn Russell booting eight points.
Russell, Ali Price and Lamont scored tries for Glasgow after the interval, while two penalties from Ronaldson and one from John Cooney were all Connacht mustered in the second half.
Connacht went ahead in the fifth minute through Adeolokun after full-back Tiernan O'Halloran twice made breaks.
Within eight minutes, however, Glasgow had taken the lead. First a penalty was kicked by Russell, then full-back Stuart Hogg pounced on a loose ball and kicked it upfield where Glasgow pressure ended with hooker Flynn being driven over and Russell converting.
As the first quarter ended O'Halloran made another break, continued by centre Ronaldson who kicked a penalty.
Connacht dominated possession and their slick handling brought a second try after 30 minutes. Lock Andrew Browne made the breakthrough and number eight Muldoon went over in the corner. Ronaldson converted to put his side 15-10 ahead.
Glasgow responded with a second Russell penalty and resisted a late charge to go in two points down.
Although Connacht's Ronaldson kicked a second penalty soon after the restart, Glasgow soon took the lead with Russell finishing at the posts and then converting.
Five minutes later Connacht number 10 Jack Carty received a yellow card from referee Ian Davies for a high tackle on Glasgow centre Pete Horne. From the penalty, taken as a scrum, Price scored and Russell converted.
Swinson's red card was followed by Ronaldson kicking a penalty to ease Connacht closer, but the home team had a final push to come.
Horne kicked a penalty, and although Cooney responded in kind, veteran winger Lamont sprinted to the line for Glasgow's fourth try two minutes from time.