First-half tries from Marcus Guthrie and two from Duncan Gray, with two conversions from Graham Poke, gave Orkney a 19-5 lead at half time, the Penguins having to settle for an unconverted try.
It was Scott Rendall who got Orkney's fourth try in a second half that had a few quiet spells, but bursts of action from both sides.
Two late unconverted tries from the Penguins were followed in the final minutes by another great Orkney move. Willie Thomson broke through the middle and offloaded to Philip Ross to make a signature dash for the line.
It made it 38-15 as the final whistle sounded to cheers from the 350-strong home crowd, who had been well entertained.
More photos from the match available at Orkney Photographic & Ollie Laughton