A clever, streetwise, clinical win for Glasgow – the kind of performance and result they have so often struggled to produce in the past.

Gregor Townsend's side absorbed all sorts of punishment for three quarters of the game, but they weathered the home storms and closed out with a brace of tries in the final 20 minutes by Tommy Seymour, the wing brought into the Scotland squad last week.

There were doubts over both scores, but you make your luck on the road and you take it with no questions asked. This was Glasgow's fifth consecutive RaboDirect PRO12 victory, and they did it in a place that has been a graveyard for more vaunted sides in the past. They may be dead in the Heineken Cup water, but they are steaming ahead rather nicely in this competition.

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Glasgow's injury list, routinely described as crippling, hasn't done Mike Cusack much harm. The Yorkshireman's promotion from third to first in the tighthead pecking order has done wonders for him as well as bringing Glasgow a stream of set-piece penalties. It was the smallest surprise of the opening stages here that the first scoring opportunity was a Jackson penalty effort – it barely cleared head height – that Cusack had won in a scrum. Jackson overcame that early miss to nudge Glasgow ahead with a penalty – again won in the scrum – in the 11th minute, then added a second four minutes later.

However, while Cusack won penalties on one side of the scrum, Ryan Grant gave them away on the other and Glasgow struggled to build momentum. Instead, the initiative was stolen by Treviso when Manon Vosawai steamed over from a 22nd-minute lineout for the game's first try.

In sometimes filthy conditions it was no great surprise that both sides were happy to put air beneath the ball, but there was a distinct impression that Treviso gained their yards more easily in that aspect of the game. Glasgow, by contrast, found territory harder to come by, although you had to credit their hosts for doing a good job of pinning them back.

Vosawai's fierce running also tied up the Glasgow defence at times, but they did rally to stage a brilliant break of their own six minutes from the break. It came from an innocuous position near halfway, when Niko Masawalu spotted a tiny gap down the left side and duly threaded himself through it. Henry Pyrgos carried on the move, hacking ahead and sprinting for the line. Pyrgos lost the race, but he seemed to have a strong case for obstruction.

At the interval, reflecting on a half in which they had been hammered for territory, Glasgow could feel reasonably satisfied with a scoreboard that showed them just four points behind, 10-6, after Kris Burton had added a penalty to his conversion of Vosawai's try. Yet while that modest gap was a reflection of their resolve in defence, it also measured the degree of good luck they had enjoyed along the way. Clearly, something better was going to be required after the break. Cutting the deficit to one point was certainly a good start, Jackson clipping his third penalty between the sticks after the Treviso forwards had poured through a lineout three minutes after the restart. It must also have warmed Glasgow hearts to steal possession from a Treviso attacking lineout just five yards out a few minutes later.

At that stage neither side seemed to have the wherewithal to summon a critical breakthough. Glasgow, however, despite being slightly under the cosh, actually took the lead in the 56th minute when, on a rare foray into the Treviso half, they earned a penalty in a ruck and Scott Wight, who had just replaced Jackson, steered it over. The advantage was short-lived as Treviso stole it back with a Tobias Botes penalty soon afterwards, but in the 65th minute Glasgow grabbed the game-breaking try through Seymour.

It was more of a horror show for Treviso as they twice guddled the ball as they tried to move it along the backline in their own 22. When it spilled the second time, Seymour hacked on and raced after it. His touchdown looked weak, but the TV official ruled the try good.

Staggeringly, the score came after they had been reduced to 14 men by the sin-binning of Tim Swinson for collapsing a drive. More staggeringly still, they then grabbed another try, Seymour again the finisher after a brilliant crossfield kick by Wight.

Robbery? Maybe. But all the great sides have had a larcenous streak. They might remember this one as the game where Glasgow grew up.

Treviso: L McLean; C Loamanu, T Benvenuti, A Sgarbi, T Iannone (B Williams, 64); K Burton (F Semenzato, 43), T Botes; I Fernandez-Rouet (M Rizzo, 54), F Sbaraglini (L Ghiraldini, 40), P Di Santo (L Cittadini, 38), F Minto, C Van Zyl (captain; A Pavanello, 54)), S Favaro, A Zanni, M Vosawai.

Glasgow: P Murchie; T Seymour, S Hogg, A Dunbar, N Matawalu; R Jackson (S Wight, 54), H Pyrgos; R Grant, F Gillies (D Hall, 40), M Cusack (O Fainga'anuku, 70), T Ryder (T Swinson, 54), A Kellock, R Harley (J Eddie, 60), J Barclay, R Wilson.

Referee: L Colgan (Ireland)