Speaker Nancy Pelosi recalled lawmakers to Washington over objections from Republicans dismissing the action as a stunt.
President Donald Trump urged a no vote, including in a Saturday tweet, railing against mail-in ballots expected to surge in the Covid-19 crisis. He has said he wants to block extra funds to the postal service.
“Don’t pay any attention to what the president is saying, because it is all designed to suppress the vote,” Ms Pelosi said at the Capitol.
She called the postal service the nation’s “beautiful thread” connecting Americans and said voters should “ignore” the president’s threats.
The day-long session came as an uproar over mail disruptions puts the postal service at the centre of the nation’s tumultuous election year, with Americans rallying around one of the nation’s oldest and more popular institutions.
Millions of people are expected to opt for mail-in ballots to avoid polling places during the coronavirus pandemic.
Ahead of voting the president tweeted: “This is all another HOAX.”
More than two dozen Republicans broke with the president and backed the bill, which passed 257-150. Democrats led approval but the legislation is certain to stall in the GOP-held Senate. The White House said the president would veto it.
Facing a backlash over operational changes, new Postmaster General Louis DeJoy testified on Friday in the Senate that his “No. 1 priority” is to ensure election mail arrives on time.
But the new postal leader, a Trump ally, said he would not restore the cuts to postboxes and sorting equipment that have already been made. He could not provide senators with a plan for handling the ballot crush for the election.
Mr DeJoy is set to return on Monday to testify before the House Oversight Committee.
The bill would reverse the cuts by prohibiting any changes made after January and provide funds to the agency.
In a memo to House Republicans, leaders derided the legislation as a postal “conspiracy theory” act. Many GOP lawmakers echoed such sentiments during a lively floor debate.
Nevertheless, Senate Republican leader Mitch McConnell is eyeing a 10 billion dollar (£7.6 billion) postal rescue as part of the next Covid-19 relief package.
While Mr Trump has said he wants to block emergency funding for the agency, the White House has said it would be open to more postal funding as part of a broader bill.
