Leading an opposition day debate on education and social mobility, Ms Rayner urged ministers to drop plans to expand the grammar system.
She called for a more wide-ranging approach to improving standards.
Education Secretary Justine Greening said grammars boosted social mobility.
Speaking in the Commons, Ms Rayner  said: "The purpose of today's debate is to send a message that members of all parties are committed to an evidence-based approach to education policy and not pursuing the failed policy of academic selection - because we know that this policy is not the answer to Britain's social mobility crisis and the government knew that too until very recently."
She said: "Already in the consultation document launched in November, the government pledged Â£50m to help existing grammar schools expand.
"The same green paper made a series of substantial un-costed pledges to those schools that want to become grammars, or the academy chains that want to open them.
"Now, just this weekend, government sources have briefed the Sunday Times that there will be tens of millions more to help grammar schools expand.
"The idea that this is the way the government should spend taxpayers' money is simply baffling when nurseries across the country are facing closure because the government will not deliver the investment needed to deliver on their manifesto pledge to deliver 30 hours of free childcare a week, when our schools are facing deeper cuts in their budgets than any time since the 1970s."
But Ms Greening said the expansion of selective education could help promote social mobility.
"In reality, as challenging as it is for our country, there is no country in this world that has managed to crack the issue of social mobility yet," she said.
"The reality is that grammars can have potentially a transformational impact in some of the most deprived communities where we want to see the biggest changes."
Later in the debate, Conservative MP for Croydon South, Chris Philp, spoke of "the terrible, terrible unfairness that in our system today, very often, the only way to be sure of an outstanding education is to pay for it - either by going private or buying a much more expensive house in the catchment area of a good school".
He said: "And it is a disgrace that the only way to be sure of an academically elite education is to pay for it today."
Mr Philp also cited evidence he said suggested children from "ordinary" backgrounds did better in grammar schools.
White boys from under-privileged backgrounds who attended a grammar school had a "30% higher chance of going to university" than those who did not," he said.
But former shadow education secretary Lucy Powell accused him of "absolutely rubbishing" the existing  system.
Intervening in Mr Philp's speech, Ms Powell said: "I think any parent or teacher watching this and hearing somebody from the government benches saying that the only way to guarantee an excellent education is to pay for it is absolutely rubbishing our excellent education system."
Former Tory cabinet minister and MP for Wokingham John Redwood said new grammar schools were a good idea because talented young footballers and musicians were selected at a young age to hone their talents.
He said: "When I asked the shadow secretary of state whether she was upset by the fact that our elite sports people have usually been selected at quite a young age for special training, special education, and that they are expected to achieve to a much higher level than the average and they are given training and made to do extra work in order to do so, and she didn't seem at all upset by that in any way."
Labour MP Stella Creasy suggested the England football team's performance could be better if it had more players from comprehensive schools,
Intervening, Ms Creasy said: "I'm glad you mentioned football because actually 13% of our national football team went to a private school, which is double the number of children who go to private schools nationally.
"Do you think that might account for the performance of our national football team, if we're missing out on the talent that exists in the comprehensive sector?
"And will he recognise that that is precisely the problem that we're looking at today? We're missing out on talent as a result of too narrow a focus."
Labour's motion, which said there was no evidence that extra academic selection would improve social mobility, was defeated by 310 votes to 263.
A government amendment welcoming its continuing consultation on schools was approved unopposed.
Allocating cash for the expansion of grammar schools in England when other parts of the education sector face funding concerns is "baffling", shadow education secretary Angela Rayner says.