Ashley Beck and Rhys Webb also went over for the hosts and Dan Biggar kicked nine points as they look to stave off Glasgow’s top-four challenge.
The Blues could only muster three penalties from fly-half Gareth Davies as co-caretaker coaches Paul John and Dale McIntosh endured a difficult first game in charge.
The Ospreys, who had lost three of their previous four Pro 12 fixtures, are now unbeaten in 13 league games against the other Welsh regions.
The Blues have now lost five in a row and remain without a win on the road in the Pro 12 this term.
Beck claimed the opening try in the 10th minute. Skipper Alun Wyn Jones and flanker Justin Tipuric, back from Six Nations duty with Wales, kept the ball alive for the centre to profit out wide, with Biggar adding the conversion.
The Blues hit back through Davies’ boot but were soon on the back foot again, with Natoga beating Alex Cuthbert to Webb’s clever grubber.
Another two Davies penalties at least kept the Blues in the game, but a high turnover count was proving costly and a third Ospreys try soon arrived as lovely hands from Sam Davies freed Natoga for a simple finish, with Biggar converting.
The bonus-point was secured early in the second half when Webb snuck through a gap on the fringes to dot down.
Biggar was on the mark with the extras and a penalty before Natoga rounded off the scoring, riding Cuthbert’s tackle score in the corner.
A difficult night for the Blues was compounded when wing Harry Robinson was stretchered off after suffering a nasty ankle injury.
