Several witnesses rushed to douse the plane's flames and pull out the two women, the only people aboard. A man who helped was treated for minor cuts and burns, but no one on the ground was hurt by the crash itself.
The single-engine 1988 Mooney M-20L went down Wednesday in a parking lot that serves a Costco and a Target store in the Kearny Mesa neighborhood.
The plane bounced while landing at nearby Montgomery Field, continued westbound and went down, said Ian Gregor, a spokesman for the Federal Aviation Administration.
However, helicopter pilot Vince Carter said he had taken off from the field when he heard the pilot tell the control tower in a radio transmission that she had lost power on takeoff.
"She said she lost power and she was going down and that was it," he told KFMB-TV.
There was no immediate way to resolve the two reports.
The plane clipped the top of the Target store and knocked down a light pole, police Lt. Steve Behrendt said.
It spun around and finally landed in the parking lot in a loading dock area away from the main entrances, and no cars were there, city fire spokesman Lee Swanson said.
The plane caught fire, but the flames were quickly doused. He said the passenger had serious burns and died at a hospital.
The pilot also had major injuries, he said. However, Behrendt said she was expected to survive.
Eyewitness: A Loud ThudGregg Smith was working in a nearby office building and saw the plane in trouble. It nearly hit his building, he said.
"I knew they didn't have enough power to do the things they needed to do," he told KNSD-TV. "I knew it was going down."
Smith said the plane left his view at that point, but he heard a loud thud and then the crash.
"The next thing I saw was a bunch of black smoke," he said.
Smith said he ran outside as he called 911.
He said 15 to 20 people were standing around the plane, some with fire extinguishers, and they managed to get the fire out before it reached the plane's fuel tank and pull the women out.
Television news reports showed the white plane appeared to be mostly intact, but its nose and one wing were torn up.
"The front of the passenger compartment, the engine is essentially broken off," Swanson said. "The landing gear is off, it's lying flat on its belly. There's some debris for several yards in each direction."
Helicopter pilot Vince Carter, who was in the air at the time and heard the pilot's last radio transmissions saying she was going down, said things could have been much worse.
"This is a miracle and testament to her skill as a pilot," he told KNSD-TV. "This could have very easily killed a lot of people. You could imagine, just shopping at Target, and a plane comes through the roof full of fuel."
"She stalled it out pretty much perfectly in the only spot she possibly could have," he said.