The House of Representatives voted 32-28 to repeal the law, which provides no exceptions for abortions even in cases of rape or incest.
Three Republicans crossed party lines to join all 29 Democrats in voting for the repeal.
The Arizona Senate, where Republicans hold a slim 16-14 majority, could vote on the measure as early as May 1.
"I'm thrilled the House has finally decided to do the right thing and repeal the archaic 1864 near-total abortion ban," Governor Katie Hobbs, a Democrat, wrote on social media on Wednesday.
Speaker Ben Toma expressed his disappointment with Democrats' vote against the ban. (AP PHOTO)
Hobbs has said she will sign a repeal of the ban if it passes the House and the Senate.
"The decision to get an abortion, or seek any type of reproductive health care, belongs in the hands of patients, their families and their providers, not politicians," Democratic representative Oscar De Los Santos told reporters before Wednesday's session began.
For the past two weeks, Republicans in the House had blocked Democrats from repealing the law.
Speaker of the House Ben Toma, a Republican, said he was disappointed that "Democrats apparently believe that abortion should occur with no limits and no regulations".
"I fervently disagree with those who advocate for extremism through unlimited, unrestricted and unregulated abortions," Toma said.
Representative Matt Gress was the only Republican to side with Democrats in last week's failed effort to repeal the abortion ban, but he was joined by two other Republicans on Wednesday.
"As someone who is both pro-life and the product of strong women in my life, I refuse to buy into the false notion pushed by the extremes on both sides of this issue that we cannot respect and protect women and defend new life at the same time," Gress wrote on social media after the vote.
Arizona's fight over the Civil War-era abortion ban is the latest flashpoint on women's reproductive rights in the United States since the Supreme Court ended the constitutional right to abortion in 2022, leaving it up to states to decide the issue.
Conservative-led states quickly invoked strict bans on abortion within their borders.
The old law was revived by a state Supreme Court ruling on April 9, and unless the legislature intervenes, it could take effect within 60 days of that ruling, the state's Attorney-General Kris Mayes, a Democrat, has said.
Even if Democrats in Arizona manage to repeal the 1864 abortion ban, restrictions on the procedure would still be in place.
In 2022, Arizona passed a law that bans abortion after 15 weeks of pregnancy.
Democrats across the US, confident that public opinion is on their side in supporting abortion rights, have sought to elevate the issue, especially before November's presidential election.
Arizona, sharply split between Democrats and Republicans, is a key battleground state in the presidential election.
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