The Ospreys trailed 10-9 until Hook kicked his first points of the game four minutes from time.
Dan Biggar also kicked nine points as the victory denied the Scarlets a place in the play-offs and sets up a thrilling clash against Munster in Limerick next SAturday.
On the back of their worst run of results in the league since their first season eight years ago, defending chmpions Ospreys looked like a team low on confidence.
A handling error right from the kick-off set the tone for an error-ridden performance.
It was not until the 17th minute that the Ospreys finally flexed their muscles at the scrum and Biggar became only the second Ospreys player, after Gavin Henson, to pass 500 points in the Celtic/Magners League.
However it was a rare moment of celebration in the first half that saw Biggar miss three from four attempts and ended with Aironi leading 7-3 at the break.
A string of needless penalties gifted Aironi their first attacking position from where wing Danwel Demas dived over in the corner on 29 minutes.
Tito Tebaldi converted and added a penalty early in the second half as Aironi, with only one victory in the Magners League all season, threatened to inflict a first Italian victory over the Ospreys.
Biggar finally found his kicking boots during the half-time break, landing two quick-fire penalties in the space of three minutes to cut the deficit to 10-9.
Once again the Ospreys turned to Hook to dig them out of trouble, shifting him to fly half on the hour. But even the British Lion was not immune from the disease of handling errors that was proving contagious among the Ospreys ranks.
Matthew Morgan was handed his senior debut late on but it was Aironi who finished the stronger as Demas and James Marshall went close.
Against the run of play, the Ospreys were then handed a late chance and Hook kept a cool head to keep the Ospreys season alive.
