The bill -- which would require a constitutional amendment -- must now pass the N.C. House.
Sen. Tony Rand, D-Cumberland, who sponsored the bill, said this change is greatly needed.
Rand said that with a two-party state, problems could arise if the governor died and were replaced by a member of the opposing party.
"It doesn't work very well to have a lieutenant governor of one party and a governor of (another) party," he said.
He also cited the high cost of elections as another reason for the change. During last year's race, $3.8 million was spent.
Rand, who ran for lieutenant governor in 1988, added that women and minorities often have a hard time gaining representation in the state's highest offices because it is difficult for them to raise campaign funds.
"(This amendment would) make the position more available to more underrepresented groups," he said.
But Rep. John Blust, R-Guilford, is not sure whether this bill would provide a positive change for the state.
"I've got mixed feelings about it," he said.