They could not have looked for a worse start, though. Not only did they lost Sila Puafisi, the prop, in the minutes before the game but they surrendered early possession to put themselves under pressure and then gave away a try.
It looked as though scrum- half Ali Pricehad rescued them but his clearance from behind his own line did little to relieve the pressure and, after a couple of goes in midfield, Zebre spread the ball wide and Leonardo Sarto gave Glasgow a glimpse of what they are getting next season as he stepped past the remaining defence to score.
The problem for Glasgow was their handling, with scoring passes going down twice in the next couple of minutes and more mistakes allowing the Italians to relieve the pressure when it looked as though Glasgow might go through the phases.
When they did, they earned the reward, with hooker Fraser Brown, the one to make the final yard to the line but nothing could stem the mistakes, with a knock-on from a high kick presenting Zebre with the chance to run the ball at Glasgow. They gave the Scots a lesson in handling and offloading for scrum-half Guglielmo Palazzani to cross.
Worse still, they could have gone even further ahead with Gonzalo Garcia missing a long-range penalty and two more kickable chances being rejected in favour of lineouts. It did not augur well for the Scots as, for the second game running, they went into the break deservedly trailing.
On top of that, they didn’t have the usual go-to game changers like Stuart Hogg available, with a number of the top choices rested for this game, so if they were going to win this, they were going to have to do it the hard way.
They did manage to work Tommy Seymour over the line early in the second half but there had been a knock-on in the build-up, though the score was not delayed long with an unsung hero turning up trumps as Price spotted a gap at the ail of a line out and whizzed through it, beating the last man with a little shimmy to score under the posts.
By now, they seemed to have relaxed more into their rhythm and twice managed to find space in midfield to send first Seymour and then Alex Dunbar racing away into the backfield with only one defender to beat. Seymour was tracked down as he cut sideways but there was no stopping Dunbar as he took the more direct route through the final tackler.
At last it was all starting to look reasonably straightforward for the Scots as they ran through the phases and an inside ball from Dunbar to Peter Horne, his centre colleague, brought try number four and a bit of daylight between the sides.
They did have a late scare when Pat MacArthur, the replacement hooker, was sent to the sin bin for a late tackle but, with Brown off injured it hardly affected the Scots since the scrums had to go uncontested.
Once they were back to full strength again, they used the power to move the ball blind from a scrum and find space to give Taqele Naiyaravoro, the wing, the kind of chance he was never going to refuse and there was still time for Jerry Yanuyanutawa and Horne to take advantage of the tiring defence for two more scores.