Gregor Townsend didn’t know whether to grin or groan after watching his Warriors snatch their fourth Pro12 triumph on the trot.
The coach saw them dominate the bulk of the fast-flowing encounter in Parma, only to leave without a precious bonus point.
They were also forced to survive a late rally by the Italians to cling on for the win, which kept them at the top of the table.
Townsend admitted he was relieved rather than elated to come home with a win.
He said: “It was not our best performance, especially in the final quarter, but it was so important to get a victory of any kind on the road.
“When we were 24-3 up going into the last 20 minutes, we should have closed them out and it was frustrating and disappointing not to get the bonus point.”
The travelling fans were subjected to a frustrating opening 20 minutes. They watched their side dominate in terms of possession and territory but a combination of needless mistakes and robust home defence kept them out.
The complexion of the contest changed in the build-up to the break as the Warriors surged into a 10-point lead in the space of two minutes.
Scrum-half Henry Pyrgos broke the deadlock with a penalty when the Zebre markers wandered offside in their own danger zone.
Then winger Byron McGuigan cruised in for a superb try, also goaled by Pyrgos.
An accurate pass by Ruaridh Jackson put Gabriel Ascarate in space and Sean Maitland’s perfectly timed run created the opportunity for Maitland to romp over.
Zebre immediately repaired some of the damage with a penalty by Luciano Orquera.
The home troops were reduced to 14 when Salvatore Perugini was yellow-carded for blatant obstruction at a ruck but Pyrgos sent his kick wide of the near post.
Glasgow were quickly back into their stride after the restart and hooker Dougie Hall finished off a slick handling move.
Pyrgos followed up with a conversion from the touchline to open up a 14-point gap.
His effort sparked Zebre into mounting their first potent raids of the match and only a series of crunching tackles kept them out.
Maitland and McGuigan then burst back into the spotlight to put the Warriors further ahead.
McGuigan couldn’t fail to complete his double after Maitland sent a beautifully weighted chip towards the line and again Pyrgos was spot on.
That was the cue for Glasgow to make a spate of substitutions, hoping fresh legs would push them on to the bonus point but no sooner was Jonny Gray in the fray than he was sent to the sin bin for a mystery offence.
Within seconds, the Warriors appeared to concede their first score only for the video ref to equally mysteriously chalk it off.
Zebre kept plugging away and were rewarded as Samuela Vunisa broke through for Orquera to convert.
There further jitters for the Scots three minutes from time when winger Luciano Sarto grabbed a second, Orquera again on target.