Edinburgh slumped to their third loss in four Pro12 matches this season after going down away to bottom side Aironi.
Naas Olivier, who contributed 15 of his side's points, Tito Tebaldi and Nick Williams all scored tries as the Italians recorded their first win.
Kyle Traynor and Tim Visser crossed the line for the Scots and debutant Harry Leonard contributed two penalties.
But Aironi were worthy of a win that means Edinburgh are now only a point ahead of the Italians.
Olivier had opened the scoring in the 14th minute with a try that he also converted.
But Edinburgh, who defeated previously unbeaten Connacht last time out for their first victory, hit back.
A Greig Laidlaw penalty and a Traynor try put Edinburgh 8-7 ahead in the 22nd minute.
However, captain Laidlaw was unable to convert that try and, just before half-time, Aironi re-took the lead through a try from scrum-half Tebaldi.
That put the hosts 12-8 ahead at the interval, although it could have been better for the home side.
Olivier spurned the chance to give his side a bigger cushion as he failed to convert either that try - his kick hitting the post - or a subsequent penalty attempt soon after.
Olivier was back on the mark five minutes into the second half, though, as he converted Aironi's third try, scored by number eight Williams following good work by the South African himself, to put his side further in front at 19-8.
Edinburgh responded to that with a number of changes and one of the newcomers, Leonard, booted a 51st-minute penalty to reduce the arrears before wing Visser crossed for a well-worked try a minute later to bring his side back to within three points of their opponents at 19-16.
Leonard could not add the conversion and Olivier set about rebuilding Aironi's advantage with a penalty and a long-range drop-goal to make it 25-16 heading into the last 10 minutes.
The visitors managed to knock three points off the deficit with Leonard's 76th-minute penalty, but Michael Bradley's side could not get any closer in the final stages as Aironi held on for their opening win.
Despite ending a seven-match losing streak, Aironi remain bottom of the standings, while Edinburgh's bonus point provisionally lifted them up to seventh spot.
Edinburgh's next match sees them host top-placed Munster, who boast a 100% record after four fixtures.
Aironi Rugby: Trevisan, Sinoti, Quartaroli, Pizarro, Venditti, Olivier, Tebaldi, Williams, Cattina, Viljoen, Biagi, Furno, Staibano, Santamaria, Aguero.
Replacements: Favaro for Viljoen (55), Sole for Biagi (62), A. De Marchi for Staibano (58), Redolfini for Aguero (58). Not Used: Giazzon, Keats, Benatti, R. Pavan.
Edinburgh: T. Brown, Jones, Thompson, King, Visser, Hunter, Laidlaw, McInally, Grant, Denton, S. Turnbull, Cox, Knight, Lawrie, Traynor.
Replacements: Scott for Thompson (66), Leonard for Hunter (45), Leck for Laidlaw (45), Watson for McInally (73), Gilchrist for S. Turnbull (45), Niven for Knight (43), Walker for Lawrie (73), Hislop for Traynor (41).
Ref: P Allan (SRU)