The loss soured for the Eels by a knee injury to Semi Radradra who is set for around a month on the sidelines.
Tepai Moeroa (shoulder), Chris Sandow (ankle) and Beau Champion (knee) are also injury concerns for the Eels.
Morris was a dynamo for the Dogs out wide, his feats matched up front from the hard-running Ma'u who broke the game open early in the second half after the Dogs led 8-0 at the break before 28,876 fans.
But all the tackling Parramatta were forced to do early on in the match fatigued them badly at the back end.
After a deluge of possession in the first 10 minutes, eight straight sets and 81 per cent, Rona opened the scoring out wide off a lovely long ball from Moses Mbye.
Canterbury surged further ahead 10 minutes later when Morris sliced his way over.
Parramatta then worked their way back in the game, with Radradra scoring in the 34th minute.
The Fijian then went down after being bundled into touch by Josh Jackson.
Danny Wicks returned to the NRL for the first time in five years 10 minutes before halftime and was strong throughout in defence and attack.
- AAP