The Cornish forwards drove their counterparts back for three first-half scrum penalties and their dominance resulted in two decisive tries and three Hartpury yellow cards.
Pirates joint head coach Gavin Cattle handed the credit to coaching partner Alan Paver.
"Paves puts a lot of man hours into that and it was nice to see them get the reward," said Cattle but he admitted: "We lacked that little bit of sparkle."
Hartpury provided plenty of resistance in the wind and wet but Cattle added: "Physically we can live with the others. We're developing nicely."
Skipper John Stevens went over for Pirates after five minutes following a slick move but referee Joe James ruled out the try for crossing.
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