The footage was shot by Ms Pelosi's daughter, documentary filmmaker and journalist Alexendra Pelosi, who was at the Capitol to document her mother, as rioters broke in.
It emerged after being shown to the committee investigating the incident.
The video offers a fascinating behind-the-scenes look at how some of the most powerful politicians in the US tried to handle the chaos — while also expressing their anger at then-president Donald Trump over his role in the riots.
It shows Ms Pelosi and other top legislators trying to co-ordinate a response from Fort McNair military base, which had been turned into a command centre after the attack.
Footage shot at 2.23pm, when rioters had already disrupted the planned certification of the 2020 presidential election results, shows Ms Pelosi wearing a protective mask and speaking into a mobile phone.
"We have got to finish the proceedings or else they will have a complete victory," she says in the video.
At about 2.42pm, Ms Pelosi is seen telling a roomful of other legislators: "There has to be some way to mentain the sense that people have that there is some security or some confidence that government can function and that you can elect a president of the United States."
At around 3.25pm, she tells Acting Attorney General Jeffrey Rosen over the phone: "... the fact is on any given day, they are breaking the law in many different ways — and quite frankly much of it at the instigation of the president of the United States.
"Why don't you get the president to tell them to leave the Captiol, Mr Attorney General?" chimes in Senate Majority Leader Chuck Schumer, also talking into the phone.
Later in the video, when told the Secret Service had disuaded Mr Trump from going to Capitol Hill, Ms Pelosi says: "I hope he comes I am going to punch him out.
"I have been waiting for this for traspassing on Capital grounds. I am going to punch him out and I am going to go to jail and I am going to be happy."