While they are likely to slip back to third after Munster host Cardiff Blues tonight, that position represented a high for the season so far.
Ruaridh Jackson, who registered five successful kicks from five attempts – while his side scored five tries – spoke enthusiastically afterwards about the prospects for both club and country.
"Fingers crossed . . . a lot of the guys are putting their hands up at the right time," he said. "They are putting the effort in for Glasgow, which is what we're looking to do, and we know that if we do that the rewards will come.
"We want to do something special with Glasgow this year and we know we have the squad to do it.
"We've used 40 players, which shows we have the strength in depth to keep things going during the Six Nations and second place is a good place to be. We'll be looking to stay there."
With Greig Laidlaw, Jackson's only serious rival for the Scotland No.10 jersey, currently playing scrum-half for a struggling Edinburgh side that were well beaten 31-16 by Leinster last night, the latter's form will be a particular boost for Johnson, Scotland's interim head coach, and his new management team.
It was announced yesterday that Johnson has brought in Dean Ryan as a forwards coach and Stevie Scott as a skills coach to work alongside himself, his kicking coach Duncan Hodge, and Massimo Cuttitta through the Six Nations Championship.
They face the task of having to decide quickly how they want Scotland to play and who they want in their squad, and they will be assisted greatly in that matter if key personnel are in form.
Consequently, Jackson has, like his team, picked the right time to regain something approaching his best form. "It has been a real roller-coaster for me, playing against the All Blacks and South Africa then [being farmed out to] Dundee, then the derbies," the playmaker said.
"It was really disappointing to get cut for the [autumn Test against Tonga] in Aberdeen but it's been brilliant for me to have the last four games in a row to build on and get some confidence coming back to my game."
As Gregor Townsend, their head coach, admitted, Glasgow were assisted by the fact Treviso had their flanker Manoa Vosawai red-carded for a dangerous tackle on Al Kellock, the Warriors captain.
"I said to the referee, 'well done,' because Al pretty much landed on his head. We were obviously helped by the red card but it was a good win," Townsend said.