It happened after 10 a.m. in the parking lot of a Walgreens near the corner of Gessner and S. Braeswood Blvd.
The victim, 80-year-old Rosalie Cook, was stabbed in the chest outside of her car after shopping inside the store, according to Houston Police Chief Art Acevedo.
A police officer arrived a short time later and found a man inside the victim's car attempting to start it, Acevedo said. When the man refused commands and lunged at the officer with a knife believed to be 6-inches long, two shots were fired.
"The manager and everyone that saw it said the officer had no choice," Acevedo said.
Investigators were reviewing surveillance video from the Walgreens and the officer's body worn camera.
Cook died after being taken to a hospital. The man police believe stabbed her died in the parking lot.
"What really makes me angry, this suspect stabbed an 80-year-old woman, then goes down and rifles through her stuff and tries to steal her car," Acevedo said.
The ordeal began earlier with a call to police about a suspicious man at the Fiesta grocery store down the street wielding a knife and asking people for money. Officers weren't able to find the man at the time.
Moments later, a 9-year veteran of HPD arrived at the Walgreens and was flagged down by customers and staff about the stabbing victim.
The suspect, a man in his 30s, has not been identified.
Saturday's shooting death is the fifth fatality involving HPD officers since April 21.
"Where is the outrage? Don't come and talk to me about officer-involved shootings when judges keep putting these crooks out on the street again," Acevedo said.
It wasn't immediately clear if the man who died Saturday had a record of criminal history.
WATCH: Houston Police Chief Art Acevedo's thoughts on the recent officer-involved shootings
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In 2019, eight people were killed in 21 officer-involved shootings, according to statistics from the City of Houston.