All but two of Minnesota's U.S. House members voted for the measure. Republicans Michele Bachmann and John Kline voted no. The other six House members had signed on as co-sponsors.
It passed 268-148.
Kline urged the House to approve the version of the bill the Senate had passed earlier.
"A mental health parity bill that has both bipartisan and bicameral support, and it does so immediately, allowing the House to approve a real mental health parity bill this very night," Kline said Wednesday on the House floor.
But because the House did not pass the Senate version, the two bills will now go to a conference committee, where the differences will be worked out.
Wellstone's son David supported the House version, saying his father wouldn't have supported the Senate bill.
Supporters said the measure would help end the stigma of mental illness and create greater access for people needing mental health and addiction treatment. Opponents warned it could drive up health care costs and force some employers to drop insurance coverage.
Sen. Wellstone fought for the issue for years, until his death in 2002.
The White House said it favors the Senate bill because it addresses the need to treat mental illnesses with the same urgency as physical illnesses, but wouldn't significantly raise health care costs.
The House bill was sponsored by Reps. Patrick Kennedy, D-R.I., who has battled depression, alcoholism and drug abuse, and Jim Ramstad, R-Minn., a recovering alcoholic who is Kennedy's Alcoholics Anonymous sponsor.
"It's about opening up the doors and ending the shadow of discrimination against the mentally ill," said Kennedy.
The House measure specifies that if a plan provides mental health benefits, it must cover mental illnesses and addiction disorders listed in the American Psychiatric Association's Diagnostic and Statistical Manual of Mental Disorders, which is used by mental health professionals.
The Senate bill gives insurers more leeway on the types of mental disorders they would have to cover.
Rep. Phil Gingrey, R-Ga., complained the House bill would mandate coverage for such conditions as jet lag and sexual dysfunction that are listed in the psychiatric association's manual.
"Can you imagine any employer being willing to cover things like that?" said Gingrey, a doctor.
Opponents said because the House bill requires much broader coverage than the Senate bill, it would prevent some businesses from providing any mental health coverage at all.
"The House bill will put us in the awkward position of either covering everything in the professional manual or covering nothing at all," said Neil Trautwein, the National Retail Federation's health care lobbyist.
The federation, a trade association for the retail industry, favors the Senate version.
The Senate bill was a compromise reached after negotiations with businesses, the insurance industry and mental health advocates. Business and insurance groups had fought previous versions, arguing the proposals would drive up insurance costs.
(The Associated Press contributed to this report)