Aironi were the only side below Edinburgh at kick-off on Saturday after picking up just one point from their opening three matches, but the Italians emerged victorious at the Stadio Zaffanella largely due to the efforts of fly-half Naas Olivier, who contributed 15 of his side's points.
Olivier 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 and thanks to a Greig Laidlaw penalty and a Kyle Traynor try found themselves 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 - for good this time - through a try from scrum-half Tito Tebaldi.
That put the hosts 12-8 ahead at the interval, although it could have been better for the home side with Olivier spurning 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.
South African Olivier was back on the mark five minutes into the second half, though, as he converted Aironi's third try, scored by number eight Nick Williams following good work by Olivier, to put his side further in front at 19-8.
Edinburgh responded to that with a number of changes and one of the newcomers, debutant Harry Leonard, booted a 51st-minute penalty to reduce the arrears before wing Tim 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, though, 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.
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