MPs backed a new clause to the Sexual Offences (Amendment) Bill by 274 votes to 64.
While ministers have introduced safeguards into the Bill to protect vulnerable teenagers from abuse, peers are still likely to oppose the measure on the grounds of morality.
Baroness Young, who led peers' opposition when it was debated as part of the Criminal Justice Bill last July, said the legislation was still insufficient to ensure that youngsters in care would not be abused.
"I have not changed my mind... How can you when there is such a moral issue involved," said Baroness Young, the former Tory leader of the Lords.
"I have had thousands of letters of support from the public, including from the gay community... and I am looking to table amendments once the Bill reaches the Lords."
If the peers oppose the Bill, it will then go back to the Commons where MPs are likely to reverse the defeat with an overwhelming majority.
Government business managers fear this "constitutional ping-pong" could disrupt the tight legislative timetable.
But Tory sources accuse ministers of introducing such controversial legislation in this parliamentary session to give them further ammunition to scrap hereditaries' voting rights with the House of Lords Bill.
In the Commons, MPs also backed an amendment ending prosecution for children under 16 who have homosexual sex with adults over the age of consent.
At present boys and girls who engage in homosexual sex with adult partners face prosecution, whereas children of the same age who engage in heterosexual sex with adults do not.