The visitors led 14-4 when Kasiano turned the game, twice handling possession to put Morris over in the 27th minute before offloading to a runaway Josh Reynolds in the ensuing set.
The Tigers, who had key trio Robbie Farah, Aaron Woods and James Tedesco also on Origin duty, regained the lead when debutant Jacob Liddle crossed just after halftime.
They could have kicked further ahead when Tim Simona broke into the backfield a minute later, but fill-in fullback Jordan Rankin spilled an easy catch with the tryline begging.
Instead Canterbury fought back again, Morris completing his double in the 60th minute before Sam Perrett extended the Bulldogs' winning streak to four with a try on fulltime.
The loss for the Tigers, who had strong performances from Naiqama, Mitchell Moses and Tim Grant, leaves them in 11th spot, two points out of the top eight.