The Bears ran in seven tries to two including a double to Rabbitohs player Mitch Buckett.
NSW Cup debutant Dylan Walker scored a try and kicked seven goals in the 30-point drubbing.
The Bears now prepare to head across to New Zealand to take on the Auckland Vulcans in round five, to be played on Sunday 7 April at Mt Smart Stadium before the Holden Cup and NRL matches between the Rabbitohs and the Warriors.
North Sydney Bears 42 (Mitch Buckett 2, Justin Hunt, Shaune Corrigan, Chris Centrone, Jesse Roberts, Dylan Walker tries; Dylan Walker 7 goals)
Illawarra Cutters 12 (Michael Lett, D. Phillips tries; Junior Vaivai 2 goals)