Scrum-half Henry Pyrgos touched down twice and winger Nikola Matawalu once for the Warriors within the first 14 minutes, with winger Sean Maitland's second-half try securing the bonus point. The rest of the hosts' points came from the boot of centre Finn Russell.
Centre Alberto Sgarbi's 11th-minute score, converted by scrum-half Tobias Botes, and a Botes penalty soon after, was all the visitors could muster in a match which had been scheduled for December 20 but was postponed due to flooding.
It was a murky night in Glasgow, but it did not take the Warriors long to sparkle.
The Italian side were much involved in the play, but their reliance on muscle played into the hands of Glasgow's top-class defence.
Within five minutes, the Scottish side were 12-0 ahead thanks to two well-taken tries.
Pyrgos found Maitland, who, having come infield from his right-wing berth, stepped on the gas and roared close to 30 metres, through several tackles, before putting Pyrgos over for the unconverted try.
Three minutes later, after Glasgow had won a Treviso lineout, centre Mark Bennett made a long break which was finished off by the team's top try-scorer Matawalu, with Russell converting.
Treviso hit back with a spectacular try of their own on 13 minutes, off one of a number of indifferent kicks by Glasgow fly-half Rhuaridh Jackson.
Winger Angelo Esposito made a lot of ground before Sgarbi touched down, and Botes added the extras.
Botes also then slotted a penalty, before Glasgow finished the exciting opening period with a third try on 22 minutes.
Again Maitland made the hard yards before a delightful pass from Robert Harley sent in Pyrgos, with Russell converting.
Resilient Treviso then dominated territory and possession, but Botes missed with two kickable penalties.
The half closed with Glasgow again on the Treviso line, but unable to make anything of a five-metre scrum, so the hosts went in leading 19-10.
Glasgow pulled ahead with a Russell penalty on 47 minutes and, six minutes later, the bonus-point try arrived, off turn-over ball in midfield. This time Maitland was the scorer after a penetrative run by Russell, who converted from far out.
The Warriors can be highly satisfied with their evening's work, but will be aware tougher challenges lie ahead with their next two games against Munster and Ulster.