Striking a collegiate tone rarely heard at PMQs, the prime minister and the Labour leader said politicians should work together to effect change, after Ms Everard's death sparked conversations about how women feel unsafe while outside the home.
Sir Keir urged the prime minister to work with him to ensure Ms Everard's death is a "watershed moment" and a "turning point" for tackling the "epidemic" of violence against women and girls.
Serving Metropolitan Police officer Wayne Couzens, 48, is accused of kidnapping and murdering 33-year-old marketing executive Ms Everard as she walked home from a friend's flat in Clapham, south London, on the evening of March 3.
He is due to go on trial in the autumn.
Speaking in the Commons, Sir Keir said: "The awful events of the last week have lifted a veil on the epidemic of violence against women and girls.
"This must also be a watershed moment to change how we as a society treat women and girls and how we prevent and end sexual violence and harassment.
"I believe that if we work together, we can achieve that and the questions I ask today are in that spirit.
"So first, does the Prime Minister agree that this must be a turning point in how we tackle violence against women and girls?"
Watch PMQs in full:
Mr Johnson replied "yes I do", adding: "That event has triggered a reaction that I believe is wholly justified and understandable."
Mr Johnson added that the Government is doing "everything that we can" to make the streets safer for women.
He also told MPs: "But I think that (Sir Keir) is right, frankly, that unless and until we have a change in our culture that acknowledges and understands that women currently do not feel they are being heard, we will not fix this problem.
"And that is what we must do. We need a cultural and social change in attitudes to redress the balance and that is what I believe all politicians must now work together to achieve."
Sir Keir said there should be a specific new law on street harassment while the law on stalking and sentences for rape and sexual violence should be toughened.
The prime minister said the government is "always happy to look at new proposals", adding: "What we are already doing is introducing tougher sanctions on stalkers - that has already been brought in - and we are bringing in new measures to make the streets safer. Of course that is the right thing to do."
Sir Keir said "many, many" women and girls who are subjected to sexual violence "do not feel confident" to come forward and report what has happened to them, adding that support for victims must be improved in law.
He also highlighted that 1.5% of rapes reported to the police lead to a prosecution, adding: "Put the other way - 98.5% of reported rapes don't lead to a prosecution, that's a shocking statistic.
"Can the prime minister tell us what is he going to do about this, not in a few years' time, not next year, but now?"
Mr Johnson replied: "I agree with him. One of the first things I said when I became Prime Minister was that I believe that the prosecution rates for rape were a disgrace in this country and we need to sort it out."
Listen to the ITV News Politics Podcast:
Sir Keir also attacked the new policing Bill, which passed the Commons after a vote on Tuesday, saying it should be revised to include provisions which would better protect women and girls against violence.
He said the Bill "provided for longer maximum sentences for damaging a memorial" than for sentences regularly given to rapists.
He said the Police, Crime, Sentencing and Courts Bill set maximum sentences for damaging a memorial at 10 years and cited three examples of people being given less than that for raping minors.
The PM hit out at Sir Keir for not backing the Bill, saying it is a step toward addressing rape sentences.
Sir Keir said "nothing in Bill would have increased length of sentence in any" rape cases.