The visitors did it the hard way after conceding a try to winger Luca Sperandio within two minutes of kick-off and they watched Tommaso Allan and Ian McKinley butcher, between them, three very kickable penalties.
Glasgow would roll up their sleeves and carve out a handy lead and, having exerted their authority, the visitors would then put their feet up on the sofa and enjoy an afternoon nap, inviting the Italians back into contention.
Gregor Townsend’s team probably weren’t helped by a late change in the referee from an experienced Welshmen to a local whistler who made a decent enough fist of things, although a few decisions would have had the Glasgow coach scratching his head.
Stuart Hogg looked like he enjoyed his first Pro12 start in the No.10 shirt, with several booming kicks from hand, five from five off the tee and Glasgow’s opening try.
However the versatile back still takes the ball deeper than Finn Russell, with all the implications that has for his midfield who missed Alex Dunbar’s ability to straighten the line. Glasgow played some good rugby with the ball in hand but they were sluggish and lacking intensity in defence, generally looking as if they would rather be elsewhere despite the benign, Italian winter sun.
The opening half proved a horror show for No.8 Ryan Wilson, who missed a tackle for the Italians’ first try and then lost the ball in contact twice, being stripped by a back on the second occasion.
After that early Treviso try Glasgow eventually put clear blue water between themselves and their hosts with their third try of the afternoon on 25 minutes, only to make two howlers which gave the Italians another score and another burst of self-belief.
One wayward pass – it might have been by Adam Ashe – missed everyone on its way to the dead ball area and when full-back Peter Murchie went to touch it down he somehow managed to miss the ball altogether. It was classic Keystone Cops, not that Gregor Townsend would have been laughing.
Treviso threatened in attack, stand-off Allan found acres of space in the Glasgow ten channel, but the home side’s defence was in the same category as Santa Claus: non-existent. All Glasgow had to do was hold on to the ball for three or four phases and huge holes would appear. After that early try by the home team, Glasgow scored two of their own in as many minutes.
Hogg somehow held on to Allan’s grubber kick and did well to win the foot race to the Treviso line from 70 yards out.
Just minutes later Tommy Seymour finished off a move that owed everything to Murchie’s initial break and Henry Pyrgos’s canny inside support line.
The first-half tries were finished off by Ashe, who needed just one fend to find the whitewash.
Glasgow should have been out of sight at the break but penalties by Allan either side of half-time meant the Italians were trailing by just three points with half an hour on the clock. Just as the fans were fretting, Glasgow’s diminutive centre Nick Grigg showed great determination in scoring his side’s fourth, bonus-point try on the 50-minute mark, brushing aside several typically anaemic tackles by the men in the green and white shirts.
Once again Glasgow took their foot off the gas and Treviso set up camp inside the visitors’ red zone. McKinley hit the post with an absolute gimme of a penalty but he was on the money with another, so when Treviso’s lock, Dean Budd, barged over the Glasgow line on 74 minutes, McKinley’s conversion levelled the scores at 28-28.
As they had done all afternoon, Glasgow responded immediately, this time with a flowing movement that ended in Sean Lamont and Seymour combining up the left flank to send replacement Rory Clegg over the line, with Hogg having the last word of a fascinating match.