A last gasp penalty goal from Matthew Jarvis earned Connacht a stunning come-from-behind win over Aironi.
The Irish side headed into the clash in decent form, having won their last two games, while Aironi's poor season was showing no sign of improving.
The first points of the game came from Luciano Orquera, who booted over a drop-goal on 13 minutes to give the visitors the lead. But Aironi's lead didn't last long, with Miah Nikora's penalty goal minutes later levelling the scoreline.
The Italians bounced back though and by half-time they were 13 points in front.
On 23 minutes Quintin Geldenhuys scored the game's first try, which was converted by Orquera, and then two penalty goals from the Argentine fly-half ensured that Aironi headed into the interval with a comfortable lead.
Connacht needed points early in the second half to get themselves back into the game, but they had to wait until the 60th minute before they could add to their tally.
Nikora's two penalty goals took the hosts to within a converted try of Aironi and on 74 minutes they got the crucial score their efforts deserved. Rodney Ah You was the man to get over the line for Connacht, with Nikora's conversion levelling the scores and ensuring a grandstand finish.
Both sides pressed for a winning score, but Aironi's cause wasn't helped when Josh Furno was dispatched to the sin-bin.
The game looked to be heading for a draw, but Jarvis' penalty goal from his own half in the dying seconds sparked jubilant scenes at the Galway Sportsground and broke Italian hearts.
Try: Ah You
Pens: Nikora 3, Jarvis
Pens: Orquera 2
Yellow card: Furno (Aironi - 74th min)
Connacht: 15 Gavin Duffy (c), 14 Tiernan O'Halloran, 13 Kyle Tonetti, 12 Henry Fa'afili, 11 Fetu'u Vainikolo, 10 Miah Nikora, 9 Frank Murphy, 8 George Naoupu, 7 Ray Ofisa, 6 John Muldoon, 5 Mike McCarthy, 4 Michael Swift, 3 Ronan Loughney, 2 Ethienne Reynecke, 1 Denis Buckley.
Replacements: 16 Adrian Flavin. 17 Stewart Maguire. 18 Rodney Ah You. 19 Mick Kearney. 20 Johnny O'Connor. 21 Paul O'Donohoe. 22 Matthew Jarvis. 23 Eoin Griffin.
Aironi: 15 Tito Tebaldi, 14 Giulio Toniolatti, 13 Sinoti Sinoti, 12 Matteo Pratichetti, 11 Giovanbattista Venditti, 10 Luciano Orquera, 9 Tyson Keats, 8 Josh Sole, 7 Simone Favaro, 6 Nicola Cattina; 5 Marco Bortolami (cap), 4 Quintin Geldenhuys; 3 Lorenzo Romano, 2 Fabio Ongaro, 1 Matias Aguero.
Replacements: 16 Tommaso D'Apice, 17 Alberto De Marchi, 18 Luca Redolfini, 19 Joshua Furno, 20 Nick Williams, 21 Naas Olivier, 22 Gilberto Pavan, 23 Paolo Buso.
Referee: Ian Davies