In Benetton Treviso's back yard, Gregor Townsend's side delivered a masterclass in controlled and measured rugby, subduing their opponents physically in the first half, taking their points in the second, and moving themselves yet closer to the holy grail of a home semi-final in the RaboDirect play-offs.
It was a personal triumph for Scotland winger Tommy Seymour, whose quick wit and even quicker feet brought him a haul of three tries and, unsurprisingly, the man of the match award. But even Seymour would have to concede that this was, above all, a splendid collective effort, all the more impressive in conditions that made handling something of a lottery.
You almost felt for Treviso, who took heavy punishment in their last home match before an uncertain summer of restructuring. Around half the players who started last night have already confirmed their departures, and there was a suspicion at times that their hearts and their heads were already elsewhere.
This, though, takes nothing away from Glasgow, who have now won their last seven PRO12 games on the trot, and one more victory, against Zebre at Scotstoun next Saturday, will guarantee their first-ever home play-off.
Having made so many changes ahead of this game, the only problem Townsend now has is choosing which of his in-form players should step out again in a week's time.
On a grim night in the Veneto, they finally had some daylight on the scoreboard between themseves and their Italian hosts. In truth, the margin at half time probably flattered Glasgow a little, for the balance of territory and possession had been pretty equal, but there was no question that they had played a more controlled and intelligent kind of game. By contrast, Treviso displayed an urgency that, more often than not, generally led to handling errors and turnovers.
Treviso had certainly taken the game to Glasgow in the opening stages, and they were more than worth their lead when Mat Berquist clipped over his 11th-minute enalty to open the scoring. But Glasgow soon found their composure, Russell levelled things with a penalty and they then moved into a slightly fortuitous lead when Seymour took advantage of spilled Treviso possession near halfway, hacked on three times and toppled over for his first try.
His luck might have helped him, but Glasgow were settled by the score. Penalty exchanges took things along to 9-13, but in the three minutes before half-time Glasgow claimed two more penalties, extending their lead to 10 points and giving themselves the platform they needed for their second-half blitz.
And that, as it turned out, was not long in coming. Two minutes after the break, Glasgow sensed an opportunity when they set a ruck on the Treviso 22, noticed that an opponent was being treated on the turf further up the pitch, and moved the ball to the right. Treviso quickly ran out of cover and swift passing across the midfield allowed Pete Horne to put Seymour over in the corner.
Russell's imperious conversion put Glasgow 26-9 in front. Treviso had done almost nothing of any note over the previous half-hour's play and they were effectively pinned against the ropes. A few minutes later they were effectively flat out on the canvas.
The blow was delivered by a Glasgow heavyweight - prop Gordon Reid - although not in the manner expected. Five minutes after Seymour's second try, Mark Bennett, Stuart Hogg and Niko Matawalu combined to release Reid a few yards out from the line, but it was anything but a battering-ram job. With improbable deftness, the prop rounded one defender, handed off another, and stretched cleverly to score.
In a way, it summed up Glasgow's night even better than Seymour's scores.
But the winger was still to have the last word for the Warriors. His chance came in the 58th minute when Henry Pyrgos created the opening and delivered the pass at precisely the right moment. A subtle chip and a helpful bounce put Seymour clear, and he duly swept in for the bonus-point try.
Treviso deserve some credit for showing spirit to the end, but mot of their efforts were mopped up by a Glasgow defence that had tightened up consideably since its wobbly performance against Edinburgh a week ago. It was only at the very end that their were breached, and even then only in the technical sense, as referee George Clancy awarded Treviso a rather soft penalty.
It was no real inconvenience to Glasgow. They had done everything they wanted already. Next weekend, against Zebre, it is had to imagine that they will not finish the job.