The House will take a final vote Wednesday, but Tuesday's vote passed 72-47, a veto proof majority.
Since taking control of the General Assembly last year, Republicans have sought to void the 2009 law.
Earlier this month, a state House panel narrowly cleared the bill, which if passed, would strip much of the Racial Justice Act that passed the Legislature when it was under Democratic control.
Currently, the Racial Justice Act allows death row inmates to use jury statistics to attempt to prove racial bias influenced their sentences. The overhaul would demand additional evidence other than statistics to prove racial bias was a factor in sentencing.
"Our purpose is to get the focus back on the defendant, "said Republican House Majority Leader Rep. Paul Stam."Something that happened in another century in another part of the state involving other people is just not relevant."
Stam co-authored the bill.
In April, a Cumberland County superior court judge resentenced death row inmate Marcus Robinson to life without parole.
Robinson was sentenced to death in Cumberland County for the 1991 death of 17-year-old Erik Tornblom. He was shot in the head with a sawed-off shotgun after giving Robinson a ride home.
Robinson was convicted of the murder in 1994. His case was the state's first test of its new Racial Justice Act.
During that hearing, testimony was heard from a Michigan State University study that concluded racial bias in North Carolina capital cases was widespread.
"That's what the case down in Fayetteville just showed. There's a long history of racial bias in our capital proceedings in this state," said N.C. ACLU Policy Director Sarah Preston. "It basically guts the bill by making it so that a judge cannot make a decision based on compelling statistical evidence."
If passed, the new bill would disallow studies like the one from Michigan State to be presented.
There are 159 people on death row in North Carolina. Of those, advocates said 31 were sentenced by all white juries and another 38 by juries with only one minority.