Jones shot 32-year-old Fatima Lopez in the back as she tried to flee, then put the gun to the head of Estevan Catano and pulled the trigger but was out of bullets, Fresno Police Chief Jerry Dyer said.
Jones, 42, then went outside the Valley Protein plant, where he reloaded his gun, shot himself and died later at a hospital, the chief said.
The victims inside the plant did not hear the shooter because it was loud and at least some of them wore noise protectors, Dyer said.
"He had opportunity to shoot other co-workers that were in the business at this time, but he chose not to," Dyer said. "He walked around them in order to get very close to the intended targets, place the gun very close and fire a round."
Salvador Diaz, 32, was pronounced dead at the scene, and Manuel Verdin, 34, died later at a hospital. Arnulfo Conrriguez, 28, was in critical condition, and Lopez was expected to be released later from a hospital, Dyer said.
Police said they didn't know what prompted the attack by Jones midway through his shift at the plant, although other workers told police he did not appear to be himself when he arrived at the plant for work.
"There was something that must have provoked this incident, perhaps that occurred today, or maybe was building up to today," Dyer said soon after the attack.
Police said they found 24 rounds of .357 caliber ammunition - the type used in the shooting - and 21 rounds of .38 caliber ammunition at Jones' apartment.
Jones arrived at work on a bike just before 5 a.m. About three-and-a-half hours into his shift, he pulled out the handgun and began firing, Dyer said.
About 30 employees witnessed the shooting, and there were a total of about 65 people at work when the gunfire started, police said.