The measure now goes to the state Senate as the legislature holds a second special session called by Republican Gov. Rick Perry. In the first special session, a Democratic senator, Wendy Davis, held a filibuster that lasted long enough to delay a vote on an abortion bill past the deadline.
The Senate has scheduled a committee hearing Thursday.
"As a queer woman of color, I object to these proceedings," a woman in the gallery yelled as House votes were counted.
Other spectators joined her in shouting at the lawmakers as security guards escorted them outside.
The bill, like the one that failed to get through in June, would ban most abortions after 20 weeks. It would also require abortion clinics to meet the same standards as outpatient surgical centers.
Jodie Laubenberg, a Republican representative and an author of the bill, said it is "based on the pain, based on the science and technology we have now," the San Antonio Express-News reported. Laubenberg said predictions many abortion clinics will be forced to close are exaggerated.
Cecile Richards, president of the Planned Parenthood Federation of America and daughter of former Texas Gov. Ann Richards, launched a "Stand With Texas Women" bus tour, the newspaper said. She planned to visit the state's largest cities in the next few days. Davis appeared with her at a rally in Houston.