The Republican-controlled House voted 121-70 for the legislation that would alter the existing 24-week limit.
The measure would keep in place exceptions under current law for when a mother's life is at risk, or if she could suffer a serious, permanent injury without an abortion. It does not allow exceptions for rape, incest or fetal abnormalities.
Supporters said medical advances mean premature fetuses are now able to survive at an earlier point in the pregnancy than previously possible.
The strong feelings and stark language that characterizes the abortion discussion on the national level were reflected in the House debate.
"As people try to frame this debate in terms of women's rights, the question that begs to be asked is, what about the rights of those pre-born women in the womb being exterminated?" said Rep. Dawn Keefer, R-York.
Opponents argued that parents should be allowed to make their own abortion decisions with medical input and by consulting their sources of spiritual advice.
"We have to be careful in this body that we don't put an ideology on everybody and say that everybody has to live like this," said Rep. Ed Gainey, D-Allegheny.
Planned Parenthood said the bill would make Pennsylvania's abortion law among the nation's most restrictive.
Rep. Madeleine Dean, D-Montgomery, said a House that is "80 percent men and 0 percent physicians" should not be making decisions for women about terminating their pregnancies. She noted that a tiny fraction of abortions currently occur after 20 weeks.
The bill "does not protect women," said Rep. Mary Jo Daley, D-Montgomery. "It attempts to control them by imposing the views of some legislators on women, and I think that's wrong - that's morally wrong."
The legislation also would outlaw what the bill terms "dismemberment abortion," a phrase not used by medical professionals. It would effectively ban dilation-and-evacuation, a procedure that is the most common method of second-trimester abortion.
"Dismemberment abortion is completely inhumane, it's barbaric," said Rep. Kristin Phillips-Hill, R-York.
Some opponents noted that the bill had not received public hearings, while supporters said the issues have been discussed in depth for years.
Wolf, a Democrat, called the bill an assault on the doctor-patient relationship and "cruel" because it lacks exceptions for rape or incest.
"These women deserve our support, not to be maligned by politicians in Harrisburg for making medical decisions about their bodies for their families with their doctors," Wolf said in a written statement.
The bill passed the Senate in February by a 32-18 vote. The margins in both chambers raise doubts about whether supporters will be able to muster sufficient votes to override Wolf's promised veto.
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