Warriors knocked the living daylights out of Treviso then immediately became their playground chums.
Having claimed the bonus point triumph, Gregor Townsend’s stars have enlisted the help of their bruised and battered hosts in their bid to complete a two-pronged Italian job.
Glasgow square up to Zebre in Parma on Friday, when a similar result could rocket them into the Pro12 top three.
Supremo Gregor Townsend said: “We will be staying in Treviso until later in the week and spend more time with their coaches and squad.
“The guys have been allowed to have Sunday off to have a few hours in Venice and then it is back to work.
“We know the Treviso people very well and we will link up with them to learn more about Italian rugby and about Zebre in particular.
“We will have a joint training session, which will be useful to both clubs.
“Then we go to Verona for a further stint before completing the trip to Parma.”
Treviso have plenty of incentive for assisting the Warriors in any way possible as they are duelling with Zebre for the one available Italian place in the Champions Cup.
Townsend will be demanding a much more fluent start from his champions than they had at Stadio Monigo on Saturday. Their display in the first 40 minutes was ropey, to say the least, but they clicked into gear when it mattered.
He said: “To get rewards, you have to be hardworking and disciplined and we were not at the required standard before the interval.
“We were more relaxed in the second half, particularly after Stuart Hogg’s try another great bit of individual brilliance.
“It was a transformation in attitude and that was when the effort was rewarded.”
Warriors had broken the deadlock with a touchdown by skipper Jonny Gray, only for the home men to scramble their way back with two penalties from Jayden Hayward.
Glasgow responded with a Peter Horne score after great work by Henry Pyrgos.
Treviso ended the half with a flourish to create a try for Angleo Esposito and two more pin-point strikes from Hayward.
The Warriors rally started when Simone Favaro dived over against his former team.
Then Hogg underlined his remarkable talents. There seemed to be no way through, but the Scotland hero’s dancing feet left four defenders in his wake as he claimed the vital fourth try.
Grayson Hart and James Malcolm took the tally to six, four of them goaled by Finn Russell.