Carlos Joseph Ramirez, 22, had been holed up in his ex-girlfriend's house since about 6 a.m. Friday, apparently despondent over their troubled relationship.
Negotiations were proceeding calmly until shortly before 11 p.m. Saturday, when Ramirez became hysterical, police said at a Sunday morning news conference.
Police went in after hearing gunshots, reportedly lobbing several concussion bombs into the house.
Ramirez and his two-year-old daughter were found dead. His three-and-a-half-year-old died on the way to the hospital, police said.
The apparent murder-suicide came five years to the day after another Antioch man also distraught over a breakup took his son and daughter hostage then killed them and himself during a standoff.
SWAT team officers had played a waiting game with Ramirez, who barricaded himself in the home for some 42 hours. He told negotiators he was taking care of his daughters, police said Saturday.
"He threatened to kill his girlfriend and himself. He had an ongoing problem with his girlfriend" and she told authorities that he didn't want to be taken alive, said police Capt. Kitt Schwitters.
Ramirez had been named as a suspect in a warrant in the November 1995 killing of a 17-year-old during an apparent gang-related shooting in which two others were wounded. He also was accused of shooting four people in 1994, police said.
However, he remained a fugitive and was believed to have spent some time with relatives in Mexico.
The standoff began when Ramirez stormed into a back window of his ex-girlfriend's house, apparently angry over the breakup of their relationship.
Armed with at least one handgun and possibly a rifle, Ramirez fired a shot at Sam Viramontes, his ex-girlfriend's father, grazing him with a bullet. The suspect then pulled one of his daughters in front of him as a shield, police said.
The girlfriend, Cami Viramontes, and her parents managed to escape shortly after calling for help.
Dozens of black-clad SWAT officers filled the neighborhood about 50 miles east of San Francisco, some carrying sniper rifles. Police blocked off the neighborhood and evacuated 66 homes.
Frustrated by failed attempts to establish contact with Ramirez, who several times left the phone off the hook, police threw a telephone into the home Friday afternoon.
The 3-year-old picked it up, asking for her mother and telling police she and her sister were safe, police said. Ramirez could be heard in the background but refused to come to the phone, Schwitters said.
Ramirez at one point fired two rounds at officers. No one was injured.
Overnight, he also broke a front window, but it was unclear why, police said Saturday.
By William Schiffmann