They took a step closer to the bonus point when DTH van der Merwe crossed in the 62nd minute, making it 28-3, but it was not until the final minute of normal time that they had the five points in the bag.
Having only scored one try in their last six matches in all competitions, Aironi grabbed a much-needed score when Luigi Ferraro touched down with eight minutes to go.
Glasgow though had the final say, rounding off a morale-boosting win with replacement Peter Murchie going over in the corner for an unconverted try.
Speaking after his side's second win in seven league games, Glasgow boss Sean Lineen said: "To get five points is really important for the team, we needed them.
"But to score four tries from the outside backs says a lot. It was also great to see Al (Kellock) back. He's one of our real leaders and a talismanic figure."
Second row Kellock was making his first appearance of the season, after undergoing knee surgery in the summer, and played his part in a performance in which the pressure and territory Glasgow enjoyed should have seen them pick up more than four tries.
The Italian defence proved hard to unpick for long spells, but Glasgow started with a bang, camping on the Aironi line before switching the ball wide for Aramburu to shrug off a couple of tackles and grab the opening try.
Duncan Weir converted, and although Aironi raced back to the Glasgow red zone, Weir made a 60-metre clearance to put them back on the front foot.
The home scrum made a steal and number eight Ryan Wilson set up the penalty for Weir to kick from 40 metres, but then Aironi's Jaco Erasmus and Andrea Benatti pinched a couple of turnovers and give-away ball by Glasgow gave Ludovic Mercier the chance to get the visitors on the board with a simple penalty.
Scrum-half Henry Pyrgos proved a thorn in Aironi's side with a couple of kicks which tested the back three, and then his pass put Colin Shaw away on a 50-metre run which saw him halted ony inches short.
Weir booted his second penalty, and then a couple of minutes later quick thinking by Ryan Wilson with a tap penalty put Aramburu over for his second try. Weir converted and Glasgow went in 20-3 ahead at the interval.
Weir started the second half where he had finished off in the first, landing a penalty three minutes in.
But it took 20 more minutes before Glasgow could wear down the Italian defence and it took a huge effort by the home pack to put van der Merwe over in the corner.
Glasgow took their foot off the pedal and Aironi hooker Ferraro scored a well-deserved consolation try with 11 minutes remaining.
But that fired Glasgow up again and from the final play of the game, Murchie went over in the corner to secure the bonus point.
|Glasgow Warriors Score Card|
|DTH van der Merwe||1||5|
|Aironi Rugby Score Card|