The House of Lords voted last month to include 16 and 17-year-olds – but MPs rejected themove last week by a majority of 50.
“The vote in the House of Lords today means that the Bill to deliver the referendum will now pass into law before Christmas.
“The referendum will be held before the end of 2017 and rightly be based on the Westminster franchise.”
David Cameron has vowed to hold the vote before 2018
The Government has said it would cost £6 million to lower the voting age and “financial privilege” was invoked to help overturn the change to the bill in the Commons.
Justice minister Lord Faulks urged peers not to challenge the Commons again, warning that to lower the voting age might be seen as an attempt to “engineer” the result.
Opposition spokeswoman Baroness Morgan of Ely insisted 16 and 17-year-olds should be involved in a “once-in-a-generation” vote.
The Labour peer added that the outcome of the referendum “will affect them longer than any of us”.
The latest clash between the Government and Upper House came after the defeat over cuts to tax credits sparked an angry row and a review of peers’ powers.
And Liberal Democrat Lord Tyler said ministers had deliberately chosen to trigger a “financial privilege threat” in another attempt to restrict the role of the Lords.
He warned: “This is not just a casual minimalist tweak of the relationship between the two Houses.
“It is part of a much more insidious exercise to dilute our role – some would say to completely neuter the Lords.”