The Ospreys had already secured a home draw in the Pro12 play-offs but were made to work hard for this victory over Aironi in Italy.
The four-times champions stretched their recent winning streak to five in a row.
Full-back Richard Fussell and wing Hanno Dirksen crossed for a try each, with fly-half Dan Biggar kicking the rest of his side's points.
The Ospreys will play the reigning champions Munster in their semi-final.
Munster are sweating on the fitness of skipper and talisman, Paul O'Connell, who was helped off during the second-half of his side's 36-8 victory over Ulster with a suspected twisted knee at Thomond Park.
The Ospreys had already claimed a semi-final home-berth at the Liberty Stadium on Friday, 11 May, before their trip to Italy with their bonus point victory over Newport Gwent Dragons in the penultimate game of the regular season.
Aironi, who are set to lose their Pro12 franchise at the end of the season, were bottom of the table and were looking for their fifth win of the season and their first victory over a Welsh region and to sign off in style.
The Ospreys may have conceded a 22nd try of the Pro12 campaign but their defence, which is the meanest in the tournament, stood firm in the face of a typically aggressive and abrasive display by the Italian outfit in front of their home crowd.
The Ospreys were without Justin Tipuric, Aaron Jarvis, Tommy Bowe, Kristian Phillips, Huw Bennett, Will Price, Cai Griffiths, Ben John, Gareth Owen and Nikki Walker due to injury for this clash on Italian soil.
But the Welsh side couldn't have asked for a better start to the contest when full-back Richard Fussell finished off a sweeping attack to cross in the right hand corner to give his side an early lead against Aironi.
Biggar missed the conversion before Aironi's South African fly-half Naas Olivier slotted over an easy penalty for the home side to make the score 5-3 to the visitors. The Ospreys fly-half made amends for his earlier miss when he converted a penalty minutes later.
Former Munster No 8 Nick Williams, who had been on the replacements bench for Aironi's previous two games, barged his way over from short-range lineout for a try to level the score midway through the first-half.
The Ospreys replied with a long-distance try by wing Hanno Dirksen after a defence-splitting counter attack by Samoan scrum-half Kahn Fotuali'I from inside his own half to put the Welsh side 15-11 ahead at half-time.
Aironi prop Lorenzo Romano and Ospreys flanker Tom Smith were sin-binned in the second half before Biggar landed his second penalty to stretch his side's lead to seven points and one which they would not surrender.
Aironi: Paolo Buso, Sinoti Sinoti, Matteo Pratichetti, Gabriel Pizarro, Giovanbattista Venditti, Naas Olivier, Tito Tebaldi; Matias Aguero, Roberto Santamaria, Lorenzo Romano, Quintin Geldenhuys, Marco Bortolami (Capt), Nicola Cattina, Simone Favaro, Nick Williams.
Replacements: Tyson Keats for P Buso (50), Gilberto Pavan for M Pratichetti (80), Luciano Orquera for N Olivier (62), Alberto De Marchi for M Aguero (55), Fabio Ongaro for R Santamaria (55), Carlo Del Fava for Q Geldenhuys (70), Josh Sole for N Williams (62).
Not Used: Perugini.
Sin Bin: Romano (56).
Ospreys: Richard Fussell, Hanno Dirksen, Andrew Bishop, Ashley Beck, Eli Walker, Dan Biggar, Kahn Fotuali'i; Paul James, Richard Hibbard, Adam Jones, Alun Wyn Jones (Capt), Ian Evans, Tom Smith, Sam Lewis, Joe Bearman
Replacements: Tom Isaacs for A Beck (70), Rhys Webb for K Fotuali'i (62), Ryan Bevington for P James (62), Scott Baldwin for R Hibbard (55), Joe Rees for Adam Jones (52), George Stowers for I Evans (75), James King for J Bearman (59).
Not Used: M. Morgan.
Sin Bin: Evans (63).
Referee: Neil Paterson (SRU)
Assistant referees: Stefano Traversi, Simone Boaretto (both FIR)
Citing commissioner: Maurizio Vancini (FIR)
TMO: Mauro Dordolo (FIR)