The holdup in the 400 block of South Meadowbrook Drive was reported shortly before noon, according to San Diego police.
A short time later, the suspected robber crashed a car a short distance away, at Parkwood Drive and Paradise Valley Road. The man tried to set the car on fire, then fled the scene of the traffic accident and shot a man in the foot for unknown reasons.
Officers fanned out through the neighborhood in search of the robber. A SWAT team was called in to assist, Lt. Kevin Mayer said.
Administrators at Boone Elementary and Bell Middle schools, meanwhile, put their campuses on lockdown as a precaution, said Jack Brandais, spokesman for San Diego Unified School District.
At one point, the suspect knocked on the door of a home and told the resident that he had robbed a gas station and needed a change of clothes, Mayer said. The resident gave him a long-sleeve gray shirt.
At about 1:30 p.m., several officers saw the suspect and shot at him with rubber bullets, but the man managed to break through the police perimeter, Mayer said.
The gunman broke into a home in the 7400 block of Woodridge Way and took a woman hostage, Mayer said. The woman crawled out a window and escaped. At abou5 1:45 p.m., police engaged the gunman again, shooting him dead, Mayer said. It was not immediately clear why they opened fire on the man.
The lockdowns at the two schools were lifted at 2:15 p.m.