Aironi came desperately close to scoring back-to-back victories on Saturday but just fell short against Glasgow, losing 17-16 in Italy.
With the Italian side 6-3 ahead, two converted tries by full-back Peter Murchie and back-row Ryan Grant saw the Scottish side build up an unassailable lead.
Inspired by fly-half James Marshall, Aironi fought back but it wasn't enough to gain successive victories after their morale-boosting win over Connacht last week.
The first half was a war of attrition despite scrum-half Tito Tebaldi opening the scoring with a penalty. Glasgow couldn't take advantage of back-row Josh Sole's yellow card soon after but they managed to level in the 28th minute when Ruaridh Jackson kicked over three points.
Tebaldi then restored the hosts' lead before the Scottish side scored the first try of the match as Murchie touched down with Jackson converting, to leave the score 10-6 to the away team at the break.
Looking to wrestle control of the match, Glasgow made a raft of substitutions and that seemed to work as they extended their advantage through a Grant try, Jackson once again adding the extras.
However, buoyed by their first ever Magners League victory last week, Aironi got themselves back into the game when Marshall went over for his own converted score.
Marshall then got the Italian side to within one point from another penalty. It was substitute Glasgow ten Duncan Weir who had the last opportunity, but his penalty missed the target.
Pen: Tebaldi 2, Marshall
Tries: Murchie, Grant
Aironi: 15 Giulio Rubini, 14 Giulio Toniolatti, 13 Gabriel Pizarro, 12 Matteo Pratichetti, 11 Danwel Demas, 10 James Marshall, 9 Tito Tebaldi, 8 Nick Williams, 7 Nicola Cattina, 6 Josh Sole, 5 Marco Bortolami (c), 4 Joshua Furno, 3 Fabio Staibano, 2 Roberto Santamaria, 1 Alberto De Marchi.
Replacements: 16 Fabio Ongaro, 17 Salvatore Perugini, 18 Luca Redolfini, 19 Quintin Geldenhuys, 20 Jaco Erasmus, 21 Pablo Canavosio, 22 Gilberto Pavan, 23 Riccardo Bocchino.
Glasgow: 15 Peter Murchie, 14 DTH van der Merwe, 13 Federico Aramburu, 12 Graeme Morrison (c), 11 Alex Dunbar, 10 Ruaridh Jackson, 9 Henry Pyrgos, 8 Richie Vernon, 7 Ryan Wilson, 6 Robert Harley, 5 Tom Ryder, 4 Aly Muldowney, 3 Moray Low, 2 Pat MacArthur, 1 Ryan Grant.
Replacements: 16 Dougie Hall, 17 Jon Welsh, 18 Kevin Tkachuk, 19 James Eddie, 20 Johnnie Beattie, 21 Colin Gregor, 22 Duncan Weir, 23 Hefin O'Hare.
Referee: Alain Rolland (IRFU)