Michael Adebolajo, 28, and Michael Adebowale, 22, drove their car directly at Lee Rigby of the Royal Regiment of Fusiliers, lifting his body onto the hood and slamming it to the windshield, prosecutor Richard Whittam said.
Whittam said the defendants then dragged his body to the middle of the road, so that everyone could see the impact of their actions.
"They both attacked the motionless body of Lee Rigby," Whittam said. "He was repeatedly stabbed and it appears it was Michael Adebolajo, the first defendant, who made a serious and almost successful attempt to decapitate Lee Rigby with multiple blows to his neck made with the meat cleaver."
Gasps were first heard - and then silence - at London Central Criminal Court as security camera images played.
Whittam showed video of Adebolajo agitatedly talking to the camera and saying that his actions were revenge for British troops killing people abroad. He waved a cleaver and a knife. His hands were bloody.
"An eye for an eye, and a tooth for a tooth," he said repeatedly on the video.
The two men have pleaded not guilty to murder charges, though jurors were told that both men have admitted possession of a firearm with intent to cause fear of violence. The defense will present its case later in the trial.
The two are also accused of attempting to murder a police officer on the same day, and conspiracy to murder a police officer on or before May 22 - the day Rigby was attacked.
Both men sat quietly in the dock, watching the video being presented as evidence and sometimes looking down. Adebolajo clutched a copy of the Quran as Whittam began.
The video also included scenes of Rigby's final movements, showing him entering a train station the day he died, wearing a sweatshirt for Help for Heroes, a charity devoted to injured servicemen and women.
Describing the aftermath of the attack, Whittam contrasted the scene marked by "heinous behavior" to the "bravery and decency" of members of the public who came upon it.
"One woman went to the lifeless body of Lee Rigby and stroked him to provide some comfort and humanity to what had unfolded. Others went to see if they could provide first aid," Whittam said. "Another woman engaged Michael Adebolajo in conversation despite the fact that he was still holding the meat cleaver and his hands were covered in blood."
The attack raised questions about whether Britain's intelligence services could have done more to prevent Rigby's killing, as both suspects had been known to them for some time from earlier inquiries.