Both sides relied on penalties to run up their scores in the opening half. There were few good attacking drives from either side, with the visitors edging the first 40 minutes 6-3.
After a cagey start to the second half, Ospreys took control of the match, Tom Isaacs scoring a try to open up a lead for the Welsh side.
It looked like Isaacs's effort would be enough, until a devastating display from Treviso in the final five minutes saw the hosts score two late tries to overturn Ospreys' lead.
The result has little bearing for either club, with neither side having been able to make the quarter-finals ahead of today's game.