Morrison served as a language advisor on Jane Campion's acclaimed "The Piano" (1993) before landing his star-making role in "Once Were Warriors". He had been appearing in a heartthrob role on a New Zealand TV series when he auditioned for the role of Jake. Once cast, he undertook an intensive physical program to increase his body weight and bulk. Delivering a powerhouse portrayal of an irresponsible, fiery brute, the actor also endowed the character with charm and sexuality. There was a palpable heat between Morrison and his co-star Rena Owen who played his put-upon wife Beth, making their relationship believable despite his character's abuse.
Based on the international success of "Warriors", Morrison made the leap to Hollywood films, but the roles were substandard and the films were box-office flops. He was virtually wasted as Pamela Lee's love interest in the execrable "Barb Wire" (1996) and fared no better (although was unrecognizable) as one of the half-human, half-beast servants to Marlon Brando in the ill-advised remake of "The Island of Dr. Moreau" (also 1996). Just when it appeared Morrison's US career might be doomed, he landed a major supporting role as an officer on a hijacked luxury liner in Jan De Bont's highly anticipated sequel "Speed 2: Cruise Control" (1997). Despite a strong first weekend, however, the film was generally perceived as an underperformer.