Glasgow picked up just a sixth Magners League success of the season by beating Aironi at the Stadio Luigi Zaffanella.
The Warriors led 10-6 at the interval, with full-back Peter Murchie crossing for a try.
A converted try from James Marshall then had the Italians 13-10 to the good in a bruising contest.
But Ryan Grant's try, converted by Ruaridh Jackson, put the visitors back in front, meaning a penalty from Marshall was not enough for the hosts.
The narrow victory lifts the Warriors up to 10th place in the Magners League, two points clear of Benetton Treviso and 21 clear of Aironi.
Federico Aramburu offloaded for Murchie to cross the line as Glasgow took control at the end of the first half, Jackson adding a conversion to his earlier penalty.
Grant, in amongst a ruck of players, forced the ball over and Jackson again obliged with the extras.
Marshall's solo effort, conversion and penalty added to Tito Tebaldi's brace of penalties and though the Italians ultimately succumbed to defeat, the closeness of the score gives the basement side a bonus point.
Aironi Rugby: Rubini, Toniolatti, Pratichetti, Pizarro, Demas, Marshall, Tebaldi, A. De Marchi, Santamaria, Staibano, Furno, Bortolami, Sole, Cattina, Williams.
Replacements: Ongaro, Perugini, Redolfini, Geldenhuys, Erasmus, Canavosio, Pavan, Bocchino.
Glasgow: Murchie, van der Merwe, Aramburu, Morrison, Dunbar, Jackson, Pyrgos, Grant, MacArthur, Low, Muldowney, Ryder, Harley, Vernon, Wilson.
Replacements: Hall, Welsh, Tkachuk, Eddie, Beattie, Gregor, Weir, O'Hare.
Referee: Alain Rolland (Ireland)