Police were called to the woman's mobile home after receiving a 911 call about a woman suffering chest pains.
But when officers arrived, the woman pointed a gun at them and threatened to shoot anyone who came near her.
The woman stayed put despite police using flash grenades and tear gas.
The standoff in the town of Topanga, near Los Angeles, finally ended early on Friday after the woman attempted to crawl under her mobile home and police pulled her out.
"It's very unusual, but we're just happy that we're able to bring this to a peaceful resolution," said Lt. A J Rotella of the Sheriff's Department's Malibu station told the Los Angeles Times. "No-one wants to see an elderly woman, for whatever reason she acted this way, no one wanted to see her get seriously hurt."
It was unclear whether the crisis-negotiation robot was damaged in the incident. The woman also hit it with a broom and threw a cover over it.
Some police departments in the US use the robots - equipped with two-way radios and cameras - to scout dangerous situations and establish communication between police and suspects.

The £21m road, which will link the west and east of the town, was supposed to be finished by March.
However, last winter's heavy rain meant contractors could not start building a bridge over the River Tone and the Bridgwater and Taunton Canal.
Richard Needs, from Somerset County Council, said it had also encountered other challenges during the project.
He said work to lift an existing bridge over Station Road had to be delayed as workers had found the ground conditions softer than expected.
"It's not a question of moving the bridge, it's working out what are the best foundations for the new bridge to be," Mr Needs said.
"As with all construction projects there are very difficult times and there are happy times... it changes from day-to-day but overall we're making good progress and we're getting there eventually."
The one-mile-long (1.6km) road is designed to divert traffic around the north of the town and will run from Priory Bridge Road, over the river and canal, alongside the railway to Staplegrove Road.
It is hoped the new road will divert traffic away from the town centre and Priorswood Road and help with the regeneration of the Firepool area.

The council said a decision would be made on the Princes Jetty location on Princes Parade after a feasibility study later this year.
Plans for a terminal in the Cunard Building were scrapped in 2014, because of an estimated cost of up to Â£15m.
The city last hosted regular transatlantic crossings in 1968.
An existing terminal at Princes Parade is estimated to have generated Â£7m for the Liverpool economy last year, the council said.
Liverpool Mayor Joe Anderson said: "The temporary cruise liner building has been a tremendous success and served us well, but a city of Liverpool's standing and ambition needs a permanent building if we are to continue the growth we've seen in recent years."
He added the cost of any development at Princes Jetty would be offset by the passengers' economic impact.
But he stressed there was "lots of work to do before we can give any scheme the green light".
A council spokesman said there had been "a doubling in the number of vessels visiting Liverpool" - from 31 to 61 - since they were able to turn around in the city's waters in 2012.
"Passenger numbers are up from 38,656 four years ago to an expected 86,365 this year."
The council has commissioned a study "into the design and cost of constructing a terminal capable of handling 3,600 embarking and disembarking passengers with baggage - twice as many as the existing facility", he added.
Cunard director Angus Struthers said it would examine if it could "incorporate Liverpool into Queen Mary 2's iconic transatlantic crossings" if the terminal plans are approved.
Liverpool hosted the headquarters of Cunard from its launch in 1840 until the 1960s, when it moved to Southampton.
A final decision is expected to be taken later this year.
An elderly California woman has surrendered to police after a 22-hour stand-off, in which the woman shot at a police robot that was sent to communicate with her.
[NEXT_CONCEPT]
The completion date for a new road in Taunton has been delayed.
[NEXT_CONCEPT]
Liverpool has identified the preferred site of a proposed permanent cruise terminal that could see transatlantic crossings return to the city.