In her first outing since her run to the fourth round at Wimbledon, the British number one was facing an early exit in Carlsbad, California, at 6-4 5-4 down.
But Robson, the Olympic doubles silver medallist along with Andy Murray, dug deep and turned things round, losing just two more games on her way to securing a place in the second round.
There, she will face Petra Kvitova, the world number seven. Robson, ranked 25 places lower, has a winning record against the Czech former Wimbledon champion, having beaten her in their only previous meeting in the second round of the Australian Open earlier this year.
Robson finds herself in the same half of the draw as second seed Agnieszka Radwanska, who has a bye into the second round, where the Pole meets Daniela Hantuchova, who double bagelled Tamira Paszek 6-0 6-0.
Victoria Azarenka heads the top half of the draw. The Belarusian world number three plays Francesca Schiavone in her opening match in the second round.
Southern Californian Open results
Daniela Hantuchova (Slovakia) beat Tamira Paszek (Austria) 6-0 6-0
Laura Robson (Britain) beat Ayumi Morita (Japan) 4-6 7-5 6-2
Urszula Radwanska (Poland) beat Marina Erakovic (New Zealand) 7-6(3) 6-4
Sesil Karatantcheva (Kazakhstan) beat Julia Goerges (Germany) 6-3 7-5
8-Carla Suarez Navarro (Spain) beat Sachie Ishizu (Japan) 6-4 6-3
Coco Vandeweghe (U.S.) beat Allie Kiick (U.S.) 6-1 6-2