The vote was 95-34, The Dallas Morning News reported, with more than a dozen Democrats absent for the all-night debate and final passage.
Before the lopsided vote, Rep. Jessica Farrar, D-Houston, said while Republicans frame the measure as providing the best care and safety for women, it would actually limit access by tripling the cost, adding bureaucracy and going against current best medical practices.
"This will put women in jeopardy in order to obtain an abortion," Farrar said.
The American College of OB/GYNs, Texas Hospital Association and other medical groups lined up against the bill.
"If this bill is really about improving medical care, wouldn't the medical organizations support it?" Farrar asked.
"It's about putting undue burdens on women seeking safe and legal abortion."
The measure will now go back to the Senate, which is expected to accept the 20-week ban language when it takes up the bill -- and Democrats say they're prepared to do whatever they can to prevent its passage before the special legislative session adjourns at midnight Tuesday, the newspaper said.
The Senate can take 24 hours to consider the bill.
Lt. Gov. David Dewhurst, who supports the bill and presides over the Senate, has said he fears Democrats will attempt to filibuster past the deadline. He predicted if that were to happen Gov. Rick Perry would call another 30-day special session.
Under the bill, abortion clinics would be required to meet standards of surgical centers, which Planned Parenthood estimates would close 32 facilities that couldn't afford the upgrade that only five facilities now meet. The measure would also require that women take three doses of a medically induced abortion drug in the presence of a physician and that doctors have admitting privileges at a hospital no more than 30 miles away from the abortion facility.
The 20-week provision drew the most heated debate, the Morning News said. Republicans said it was based on evidence a fetus past that stage of development can feel pain, which Democrats countered as questionable.
The Morning News said Perry, a Republican, likely would sign the bill if it reaches his desk.
Democrats stalled the legislation for hours but Republicans voted to end debate 97-33 after Rep. Bryan Hughes, a Republican, brought up a motion at 2 a.m. to end the overall debate on Senate Bill 5. About 16 amendments were left unheard.
"Anyone who has been here for the last several hours would not describe this as being rushed by any means," Hughes said. "The people of Texas expect us to take a position on this bill, pro or con. We're still miles before we sleep."
Outside the chamber, Rep. Chris Turner, a Democrat, told abortion opponents, "Your being here says that the people who come to Austin who are elected officials have to be held accountable and I know you will hold people accountable in the next election. I've never ever seen this kind of outpouring on a Sunday afternoon, Sunday night, early Monday morning in late June."