Leinster (3) 21
Tries: Morris, Kearney Con: Nacewa Pens: Nacewa 3
Aironi (10) 16
Try: Williams Con: Tebaldi Pens: Tebaldi, Buso Drop-Goal: Busa
Leinster's David Kearney is tackled by Nicola Cattina
Under-strength Leinster battled back from seven points down at half-time to leave Aironi still looking for their first win in the Magners League.
Tito Tebaldi and Isa Nacewa swapped early penalties but Nick Williams' try helped Aironi lead 10-3 at half-time.
Niall Morris' try helped nudge Leinster ahead after the break and with Nacewa finishing on 11 points, Dave Kearney's touchdown made the game safe.
Aironi have lost 13 straight games in their inaugural Magners League season.
Ahead of the weekend Six Nations game, Leinster were without 11 international stars which meant a debut for Ireland Under-20 back Brendan Macken with Rhys Ruddock captaining the team for the first time.
Aironi, adrift at the bottom of the table, were minus Italy squad members Quintin Geldenhuys, Carlo del Fava, Josh Sole, Fabio Ongaro and Pablo Canavosio.
Out-of-favour Italian international scrum-half Tebaldi kicked Aironi into a second-minute lead but Nacewa replied in kind for Leinster three minutes later.
Tebaldi missed two penalty chances although the scrum-half appeared convinced that one of his efforts had gone between the posts.
Leinster suffered a blow when debutant Macken was forced off in the 14th minute because of a broken collarbone with another youngster Morris coming into the backline.
The substitution led to Leinster switches with Nacewa moving to wing and Kearney to centre and newcomer Morris stationed at full-back.
Sensing Leinster's apparent disorganisation, Aironi upped the pace and should have scored the game's opening try in the 29th minute as Kaine Robertson cut inside instead of opting for the outside as the overlap appeared on.
However, the Italians kept up the pressure and after being held up over the line, former Munster number eight Nick Williams regrouped to barge his way through Ian Madigan to notch a 35th-minute try.
Tebaldi added the conversion and only a terrific tackle by replacement Morris prevented Jaco Erasmus notching a second Aironi try before the interval.
Morris continued his impressive contribution as he ran in a superb try six minutes after the break following Richard Strauss' break and off-load.
Nacewa added the extras as Leinster started the second half in much better fettle compared to their disjointed and lethargic opening-period efforts.
Aironi regrouped to put the hosts under intense pressure before Tebaldi made a hash of a quick tap penalty to avert the danger for the home side.
The Italians did level on 57 minutes as full-back Paolo Buso slotted a superb long-range drop goal but Nacewa nudged Leinster ahead five minutes later with a straightforward penalty.
Kearney's 77th-minute try made the game safe for Leinster despite a late Buso penalty which earned Aironi a bonus point.
Leinster: Nacewa, Conway, Macken, O'Malley, D. Kearney, Madigan, O'Donohoe, van der Merwe, Strauss, Newland, McLaughlin, Toner, Ruddock, D Ryan, Keogh.
Replacements: Morris for Macken 14, McKinley for Madigan 70, Boss for O'Donohoe 48, McGrath for van der Merwe 79, Harris-Wright for Strauss 79, Shawe for Newland 67, Jennings for Keogh 48.
Not Used: O'Donoghue.
Aironi: Buso, Robertson, Pizarro, San Martin, Demas, Marshall, Tebaldi, A De Marchi, Santamaria, Staibano, Bortolami, Furno, Cattina, Erasmus, Williams.
Replacements: Pratichetti for Pizarro 70, Travagli for Tebaldi 67, A De Marchi for A De Marchi 62, Ferraro for Santamaria 64, Biagi for Furno 67, Benatti for Erasmus 67.
Not Used: Redolfini, Benettinuts
Referee: Nigel Owens (Wales)