The driver had traveled from Fresno to Los Angeles on Saturday night, then left Los Angeles shortly after 3 a.m. Sunday.
He had been on the road for about four hours when the bus overturned, officials said.
"We do have reason to believe that driver fatigue may have been a significant factor," said Lt. Dan Minor of the California Highway Patrol.
Dozens of passengers among the 44 people aboard the San Francisco-bound bus were hurt, at least seven of them with major injuries. Two passengers remained hospitalized, according to officials at Marian Medical Center in Santa Maria.
Faro Jahani, 50, of San Francisco, and Martha Contreras, a 23-year-old Santa Maria resident who was seven months pregnant, were killed in the crash, Minor said.
Rescuers were unable to save Contreras' fetus.
"They were dead before we ever got to them," said Santa Barbara County Fire Capt. Keith Cullom.
A preliminary investigation gave no indication of mechanical problems, and the bus driver did not appear to have been impaired by alcohol or drugs, Minor said.
The driver, identified as Samuel Henry Bishop, 63, of Fresno was taken to a hospital with minor injuries. No charges had been filed Sunday night.
Kim Plaskett, a spokeswoman for the Dallas-based bus line, said Greyhound drivers are trained in fatigue management and are told to immediately pull over if they are too tired to drive.
Greyhound drivers also are limited to 9½ hours of service in a 24-hour period. Plaskett said the drive from Fresno to Los Angeles is about 4½ hours, from Los Angeles to San Luis Obispo, where another driver was scheduled to take over the bus, is about four hours.
Both northbound lanes of Highway 101, one of the state's major corridors, were shut down through mid-afternoon.