In his playing days, Gregor Townsend tested the vascular fortitude of almost every coach he ever worked with, so there was a kind of perverse poetic justice as the closing moments at Scotstoun on Saturday delivered a sequence of events that must have sent his own blood pressure off the scale.

With 10 minutes remaining, and with his side 19-6 ahead, the Glasgow Warriors coach had the comfort of knowing that Leinster, typically mustard keen but misfiring in so many areas, needed two converted tries to get their noses in front. On the probability spectrum the scenario was right up there with David Cameron handing out Yes leaflets on the streets of Springburn. Yet, that is exactly what the Dublin side managed to do.

Prop Jack McGrath blasted over from close range in the 73rd minute, and Tom Denton took advantage of a Glasgow lineout howler to plough through just a couple of minutes later. Jimmy Gopperth converted both touchdowns, and suddenly ­Leinster were a point in front. Psychologically it was a crippling blow for Glasgow, or would have been had things ended up that way.

For, profligate as they had been in surrendering a seemingly insurmountable lead, Warriors showed reserves of character in their response. They muscled their way back into the Leinster 22, churned possession through the phases, and started to turn the screw. The Irish outfit were pinged for a mass offside offence and, after the ball had been wrestled away from Niko Matawalu, who had threatened a typically hair-brained tap-penalty manoeuvre, common sense prevailed and Stuart Hogg kicked the winning points.

"I did feel my heart rate rise in that last five minutes," admitted Townsend. "We had given Leinster a window of hope to get back in and it wasn't what the team deserved, because they had played so well earlier. It was fantastic of us to come back and get those three points. But, ultimately, it is just one game out of 22 that we have to play."

True, but Glasgow will be far down the road of this Guinness PRO12 season before they play another match with so much at stake. After the lesson they were given by Leinster in last season's grand final in Dublin, this result was as important as a part of their healing process as it was for the points credited to their PRO12 account.

Even if they had to crawl over the line at the end, they could reflect with huge satisfaction on the way they had built their 19-point lead in the first place. For the first 40 minutes of the game Glasgow played with a swirl and a swagger of movement, skill and self-belief. They had Leinster clutching at shadows, bamboozled by the slickness and sharpness of their play. The Warriors have played some eye-catching stuff in the Townsend era, but this took things to an altogether different level.

Following Edinburgh's startling and thoroughly deserved 14-13 win against Munster in Limerick on Friday evening, events at Scotstoun also completed a notable double, for this was the first time since 2009 that both Scottish sides had claimed wins on the opening weekend of the league competition. Of course, a long season lies ahead, but both now go into the second round of games on the front foot, which is always better than the alternative.

Glasgow's second outing is against the Blues in Cardiff on Sunday. "We've got lots to work on this week," said Townsend, the unspoken subtext of which being that almost all the material for that exercise was produced in the second half.

"But we have a good base there," he continued. "If we can sustain what we were doing in the first half for longer periods then we will be well set this season.

"It was a good game for what now happens this week. We have shown a lot of our best side in terms of speed and accuracy in contact. Defensively, I thought we were very good in the first half. Those are positives to build on. The second half was a big learning curve for us in terms of how we have to exit defence better, tackle low, keep pressure on the opposition and keep our discipline. The players realise that. Maybe we could have been further ahead at half-time, but we are never going to sit back against a team like Leinster."

Glasgow players had been careful not to bill the game as a revenge mission after their 34-12 loss to Leinster in last season's final. However, with honour satisfied, there was a little more candour in the camp, allowing players to depart from the "just another game" narrative of the build-up.

"It was a very intense week in terms of how we viewed this game," said winger Tommy Seymour. "It was no secret to them or us that this was a huge fixture to come first up after last season. To come here and put in a performance like that for the first 40 and then get the win with things to work on is a huge lift. Psychologically, going into the rest of the season, if we can iron out those mistakes and the little imperfections we showed then we will be stronger going forward."

For Glasgow, helped as they were by a dominant scrum platform, tries by Peter Horne, Jonny Gray and Josh Strauss did the damage in the opening 40 minutes. Against the side that has been their nemesis these past few seasons, it was an astonishing and uplifting way to get the new season under way. But as the second period showed, things are never that easy for very long.