The blaze, which appeared to be accidental, broke out just before 1 a.m. at 1557 159th Ave. and was under control within 10 minutes of crews arriving, fire spokeswoman Aisha Knowles said.
The man suffered critical injuries and was transported to St. Francis Memorial Hospital in San Francisco for his injuries, including first-, second- and third-degree burns to his face and chest, fire officials said. The woman with smoke inhalation was taken to Eden Medical Center, fire officials said.
Firefighters rescued a cat and a small fluffy dog from the apartment. The pets suffered heavy smoke inhalation and were taken to VCA Bay Area Veterinary Hospital in San Leandro to be treated, fire officials said.
No one else was injured.
The fire, which did not spread to the apartment's adjacent units, apparently started on a cooktop and was contained to the kitchen.
The cause of the fire remained under investigation Friday, Knowles said.
Contact Natalie Neysa Alund at 510-293-2469. Follow her at Twitter.com/nataliealund.