Glasgow were made to sweat by Zebre for a 33-28 Guinness PRO12 win in Parma.
Dries van Schalkwyk's 74th-minute converted try put the hosts five points behind and in with a chance of their first win of the league season.
But a penalty from fly-half Rory Clegg put the Warriors out of reach, with opposite number Carlo Canna kicking one of his own to earn a losing bonus point.
Canna opened the scoring with a penalty before Glasgow took a seventh-minute lead when wing Sean Lamont crossed after Lee Jones was tackled close to the line. Clegg's conversion attempt faded across the posts.
Canna landed another penalty before Clegg kicked two of his own to make it 11-6 to the visitors, but almost from the kick-off hooker Oliviero Fabiani showed fine footwork to level the score with the conversion going wide.
Glasgow retook the lead just before the break, hooker Fraser Brown scoring in the corner after fantastic work from Nick Grigg, who ran almost the length of the pitch. Clegg converted.
Grigg also claimed assists for the next two tries, scored by Lamont and Italian Leonardo Sarto. Clegg was on target with the first conversion as Glasgow went 30-11 clear.
Zebre soon pulled a try back, Thomas Boni with a grubber kick through for wing Giovanbattista Venditti to score. Canna converted.
The hosts then pummled Glasgow's line and a period of intense home pressure told when number eight Van Schalkwyk crossed and Canna added the extras.
However, Clegg's fifth successful kick at goal forced Canna to settle for his.