The committee enacted the rule 29-28, with one person abstaining. Chairman Kevin DeWine supported the rule during the contentious debate but said afterward that he was not concerned with the leadership fight, only with defeating Democrats President Barack Obama and U.S. Sen. Sherrod Brown in November.
Gov. John Kasich is reportedly backing a slate of central committee candidates in the March 6 primary who would support replacing Mr. DeWine, but the new rule is expected to prevent some of Mr. Kasich's loyalists from being seated on the committee if they do get elected.
The central committee - which also exists in the Democratic Party - is made up of one man and one woman from each of Ohio's 33 Senate districts. The committee elects the chairman, and the next election is set for January, 2013.
The new rule would require that a person have voted as a Republican in the most recent three primaries, including the current primary. One report indicated about a dozen candidates would be barred from serving.
Opponents criticized the rule as exclusionary.
"What happened to the Republican Party being inclusive? What happened to our big tent?" asked Sarah Brown, a committeeman from Stark County who said her own opponent is one who will be barred by the rule because she has never voted as a Republican.
Bob Russo, a male committeeman from Lorain County, said the tighter restrictions are needed on picking the body that runs the state GOP.
"The rule has some flaws in it but it's the best they could come up with," Mr. Russo said. He added that he has never been told specifically of a rival against Mr. DeWine, and said he hopes the new rule prevents a leadership fight from taking place.