Ospreys scored twice in the first half to take a 14-0 lead and added another two tries after the break to secure a much needed bonus-point, while the Toyota Cheetahs scored two second-half tries.
The opening quarter was closely fought as the teams tried to breach the defence with no success, but back-to-back tries for the Ospreys within four minutes - compliments of Dan Evans and Olly Cracknell – gave their team the edge in what proved to be the only points of the half.
The Toyota Cheetahs showed good intent on attack in the early exchanges, but turnovers and penalties conceded broke their momentum.
The hosts, however, came out firing after play resumed as Dries Swanepoel twisted his way through the defence to crash over, and Tian Schoeman converted.
But Ospreys cancelled this out soon after as Justin Tipuric caught the defence off-guard with a quick penalty tap, which they followed up with their bonus-point try by Cory Allen and a penalty goal to stretch their lead to 31-7.
The Welshmen were dealt a blow soon after as Adam Beard received a yellow card, and the hosts took advantage of this as Reinach Venter scored their second try from a rolling maul. The successful conversion allowed Schoeman to break the 100-point mark for the season.
Neither team was able to add to their score in the closing minutes, which allowed Ospreys to walk away with the 31-14 victory.
Toyota Cheetahs 14 (0) – Tries: Dries Swanepoel, Reinach Venter. Conversions: Tian Schoeman (2).
Ospreys 31 (14) - Tries: Dan Evans, Olly Cracknell, Justin Tipuric, Cory Allen. Conversions: Luke Price (2), Sam Davies (2). Penalty Goals: Sam Davies.