Wingers Kaine Robertson and Danwel Demas both scored their first tries in the competition, and South African flanker Gareth Krause crossed for his second of the campaign.
Connacht's sole try came from number 8 Ray Ofisa and not even the introduction of fit-again captain John Muldoon, in the closing stages, could inspire the visitors.
In warm conditions in Viadana, Aironi seized the initiative and won a five-metre scrum which Connacht managed to defend.
But that bout of early pressure yielded a seventh minute try for Rowland Phillips' men. A stray pass from Gavin Duffy was hacked on by Robertson who managed to touch down in the right corner for Tito Tebaldi to convert.
Ian Keatley replied with an 11th minute penalty, and Tebaldi drew a penalty attempt across the posts five minutes later.
Aironi, who lost 11-6 to Connacht in Galway two weeks ago, looked to have the beating of the Irish side on this occasion. They moved into a clearcut lead by the midpoint of the half, taking advantage of a defensive lapse.
Demas' grubber kick was gobbled up by Krause and touched down for Aironi's second converted try, with Connacht's rearguard caught out by the bounce of the ball.
Eric Elwood's side regained their poise and a terrific break from out-half Keatley on the right paved the way for Ofisa to dot down by the posts. Keatley's successful conversion closed the gap to 14-10.
A subsequent attack from Fionn Carr should have resulted in a sustained spell in the Aironi half, but the Italians defended well.
The home forwards were soon taking the game to the visitors again, and a knock on spoilt a promising position near the Connacht line.
Tebaldi missed a penalty just before half-time after Frank Murphy was whistled up for going offside.
Connacht's discipline was a cause for concern and when their most-capped player, Michael Swift, came in at the side of a 43rd minute ruck, Tebaldi stepped up to make it 17-10 for the league's bottom side.
His half-back partner James Marshall added a drop goal, five minutes later, to leave the home crowd in raptures.
With Ireland hooker Sean Cronin in the sin-bin for a ruck offence, Keatley kicked a penalty to claw it back to 20-13.
Aironi then lost their powerful number 8 Nick Williams to a yellow card, evening up the numbers, but Connacht struggled to create scoring chances and Keatley did not have the required distance from a penalty inside his own half.
Demas' kick through bounced favourably for Connacht and the covering Adrian Flavin was able to clear to touch. But the Connacht defence was unlocked in the 63rd minute when the South African speedster got over in the left corner for an unconverted score.
The visitors lost bustling centre Niva Ta'auso through injury and could not gain enough momentum in their hunt for a late losing bonus point.
It was Connacht's third defeat on Italian soil this season - they lost previously to I Cavalieri Estra in the Amlin Challenge Cup and Benetton Treviso in the league - and even though Aironi had flanker Josh Sole sin-binned, their strength up front and control at half-back helped them see out a famous win.
Locks Joshua Furno and Marco Bortolami gave the hosts a plentiful supply of lineout ball, combining well with hookers Roberto Santamaria and Fabio Ongaro.
Alberto de Marchi was the pick of Aironi's front rowers, with the assured Giulio Rubini impressing on his return at full-back.
|Aironi Rugby Score Card|
|Connacht Rugby Score Card|
|Ray Ofisa Treviranus||1||5|