The British number one lost the first set 6-4 and the game was into its third hour when she levelled the match in the 12th game of the second when her Japanese opponent double-faulted.
Robson broke Morita in the fourth game of the decider and won five points in a row in the next to take control at 4-1, eventually closing out a 6-2 success in two hours and 40 minutes.
Meanwhile, Coco Vandeweghe eased into the second round with a straight sets win over fellow American Allie Kiick.
Vandeweghe saw off Kiick 6-1 6-2 in just 62 minutes at Carlsbad to join eighth seed Carla Suarez Navarro in the second round of the competition.
Suarez Navarro broke Sachie Ishizu six times during the course of her 6-4 6-3 success at the Omni La Costa resort.
Poland's Urszula Radwanska was another first round winner, seeing off New Zealand's Marina Erakovic 7-6 (7/3) 6-4, while Britain's Laura Robson came from behind to beat Ayumi Morita 4-6 7-5 6-2 in two hours and 40 minutes.
Kazakhstan's Sesil Karatantcheva, a qualifier ranked 137th in the world, also advanced courtesy of a 6-3 7-5 defeat of Germany's Julia Goerges.