New Tory leader David Cameron accused Tony Blair of being "stuck in the past" in their first set-piece Commons clash.
Mr Cameron, who says he wants to move away from "Punch and Judy" politics, told the prime minister he would back his controversial education reforms.
But, after differing on selection policy, he added: "I want to talk about the future...you were the future once."
Mr Blair, facing his fifth Tory leader, said he welcomed a "new consensus" but called the Tory plans "regressive".
The question time clash came as Mr Cameron was deciding who is to get the key ministerial roles in his shadow cabinet.
Rival leadership candidate David Davis is expected to keep his job as shadow home secretary. Ex-leader William Hague is set to be shadow foreign secretary.
George Osborne is expected to stay as shadow chancellor, according to BBC political editor Nick Robinson.
Mr Cameron, 39, follows John Major, William Hague, Iain Duncan Smith and Michael Howard in taking on Mr Blair.
To the sound of Tory cheers and waving of order papers, he told Mr Blair that the first issue they would have to "work together on is getting the good bits of his education reforms through the House of Commons and into law".
The proposed reforms, which include giving schools more independence from local authorities and allowing them to become "trust schools", are unpopular with some Labour backbenchers.
He is 39 years old
Married to Samantha, one son, one daughter
Educated at Eton College and Brasenose College, Oxford
Special adviser to Cabinet ministers Michael Howard and Norman Lamont in the 1990s, then communications director at Carlton television
Became MP for Witney in 2001
Tory campaign coordinator at general election, then shadow education secretary
Mr Blair said he assumed Tories would vote for the plans, adding that it was important to give schools the freedoms they need.
Mr Cameron replied: "Absolutely. With our support you know there is no danger of losing these education reforms in a parliamentary vote."
He urged Mr Blair to allow schools to control their own admissions policies. But the prime minister said the present system should stay in place.
This prompted Mr Cameron to claim his approach was "stuck in the past", adding that "education is one of the public services in desperate need of reform".
Mr Blair countered that if schools were free to bring back selection at the age of 11, "that would be regressive".
He also urged Mr Cameron to look at the investment necessary for education reform.
Mr Cameron, who was seated next to Mr Davis, also challenged the prime minister on climate change.
Mr Blair's official spokesman said: "As far as the prime minister is concerned, it was a normal day."
Later, Mr Cameron announced the setting up of a social justice policy group to tackle Britain's "broken society", run by former Tory leader Iain Duncan Smith.
This would deal with drugs, family breakdown, crime and poor public spaces, he said.
Mr Cameron became leader on Tuesday, having beaten Mr Davis in a ballot of Tory party members nationwide. Mr Cameron received 134,446 votes to his rival's 64,398.
He has already appointed his chief whip - West Derbyshire MP Patrick McLoughlin. He replaces David Maclean, who has decided to return to the back benches.
More appointments to the shadow cabinet are expected over the next few days.