The officer, identified only as D49, said: “I instantly thought 'he's going to kill me',” of the moment one of the men ran towards her waving a weapon.
Michael Adebolajo, 28, and Michael Adebowale, 22, deny the murder in Woolwich, south-east London, on 22 May.
Earlier, the court was shown mobile phone footage of Mr Adebolajo explaining why he killed the soldier.
Mr Adebolajo and Mr Adebowale also deny attempting to murder a police officer and conspiracy to murder a police officer.
The Old Bailey also heard from an eyewitness who wept as she told the jury that she had pleaded with Fusilier Rigby's attackers to stop.
Prosecutor Richard Whittam QC read the police officer's account to jurors, in which she said: “I saw a black male running at me waving both his hands in the air in a chopping motion. In his right hand I saw what I call a meat cleaver or a machete.
“I instantly thought 'he's going to kill me'. I went to draw my Glock. Due to my position in the car, the internal door has a panel jutting out, I could not immediately draw my Glock out due to this. It was a split second decision to draw my Taser.
“I could still see the look in the suspect's eyes. They were so wide and I could see the whites of them. He was shouting something.”
She then saw a second suspect, said to be Mr Adebowale, holding a gun.
“I thought 'Oh my God he's going to shoot me'. I feared for my life,” she said.
A second officer, named in court as E48, told the jury that a man ran at the car with a knife when police arrived at the scene.
“He almost instantly broke into a sprint and I realised we were being attacked. We had very little time to deal with the threat,” he said.
Video footage of Mr Adebolajo charging towards the officers and then falling to the ground as he was shot was played to the court, then Mr Adebowale is also shot.
Officer D49 is seen keeping her gun trained on Mr Adebolajo as he lies on the ground, while E48 is seen rushing back to the police car to get a medical kit.
'Never be safe'
Mr Adebolajo earlier watched as the mobile phone footage was played to the jury, while Mr Adebowale bowed his head.
In the video, Mr Adebolajo has bloodied hands, and says: “The only reason we have killed this man today is because Muslims are dying daily by British soldiers. It's an eye for an eye and a tooth for a tooth.”
He adds “we will never stop fighting you until you leave us alone”.
“I apologise that women had to witness this today but in our lands our women have to see the same,” he says.
“You people will never be safe. Remove your governments, they don't care about you. Do you think David Cameron is gonna get caught in the street when we start busting our guns? Do you think the politicians are gonna die?
“No it's gonna be the average man like you, and your children. So get rid of them, tell them to bring our troops back so we can, so you can all live in peace.
“Leave our lands and you'll live in peace. That's all I have to say.”
His final words are an Islamic blessing.
Tina Nimmo told the Old Bailey she was a passenger in a car when she saw one of the attackers stab the 25-year-old from Manchester and drag the soldier's body into the road. She said she got out and shouted at the men to stop.
“I wanted them to stop. At the time you just get on and do what you have to do. And that's what I had to do,” she said.
A bus stopped near the scene and she warned the passengers to stay back because one of the men had a gun.
In a statement, her daughter, Michelle Nimmo, who was driving the car, said: “Throughout the attack, the two men had an evil look on their face.
“They stood around looking proud and posing with the gun and knives. They made no attempt to run away.”
The court also heard a statement from Sarah Riordan, a heavily pregnant woman near the scene who described experiencing “contracting pains” as the events unfolded. She said she had heard gunshots and had taken refuge behind a bus.
Earlier in the hearing the jury was read a letter Mr Adebolajo handed to passer-by, Amanda Donnelly Martin.
Addressed to “my beloved children”, the letter told them to seek martyrdom, and stated: “If you find yourself curious as to why carnage is reaching your own towns then know its simply retaliation for your oppression in our towns.”