Head coach Dave Rennie hailed Glasgow Warriors' "character" as they opened their Pro14 campaign with a 27-26 bonus-point win at Connacht.
The Warriors were nine points behind when Adam Hastings was shown a yellow card for a high tackle on 57 minutes.
But a thumping late drop-goal from Stuart Hogg nudged them in front, and they clung on for a narrow victory.
"The boys won that period Adam was in the sin-bin - that was crucial," said New Zealander Rennie.
"We did a lot of good stuff first-half but lacked a little bit of patience. Maybe we tried to move the ball too wide, too quickly at times and turned it over. To Connacht's credit they kept coming and every time they got down our end they got rewarded."
After Hogg's strike, Warriors were forced to watch a long-range penalty from Craig Ronaldson glance the outside of the post with the final play.
Nick Grigg was adjudged to have infringed at the breakdown, allowing Ronaldson the chance to snatch victory, but Rennie revealed Ian Davies had apologised to the Scotland centre for incorrectly penalising him.
"I would've preferred we closed the game out, but that's not the way we do things - we'll keep everyone entertained for an extra three or four minutes, unfortunately," he said.
"In the end it was a fair result with the kick missing. We know it's not how you start the season, it's how you finish. To get five points away from home is important. Some other sides will come here and struggle."