Heath, a Bremen businessman, currently serves in the Georgia General Assembly as representative of District 18. Heath won the seat two years ago when he defeated long-time incumbent Tom Murphy for the post.
Rountree, a Dallas attorney, is making his first bid in politics.
Rountree came in first in the district voting, which includes all of Polk and Haralson counties, part of Bartow and most of Paulding County.
Heath came in second in the three-way race including James Garner of Haralson County.
Rountree received 6,539 votes to Heath’s 5,215 and 5,044 for Garner in the district. Garner came in second in Polk County.
In Polk County the vote totals were not the same as the district with Heath winning by 533 votes to Garner’s 492 and Rountree’s 298.
In the district voting, Rountree got 38.9 percent of the vote, Heath had 31.1 percent and Garner received 30.0 percent of the vote.
Voters who did not cast ballots in the July 20 General Primary Election can vote in the runoff election on August 10 between Rountree and Heath.
The only voters excluded from voting in the Republican Primary runoff are those who voted in the Democratic Primary on July 20.
The winner of the runoff race between Rountree and Heath will face Democrat Lester Tate in the November General Election. Tate did not have any opposition in the primary.
Still up in the air are the Democratic race for U.S. Senate, the nonpartisan race for Court of Appeals judge and the state House District 2, according to unofficial results published Wednesday by the Secretary of State’s office.
Candidates must get a majority (50 percent plus at least one vote) to be declared a winner. When a majority is not reached, the top two vote-getters go to a runoff.
In the U.S. Senate race, Denise Majette, who took 41 percent of the vote, will face Cliff Oxford, who collected 20 percent. Third-place finisher Jim Boyd was eliminated but earned 14 percent of the vote.
The winner will face Republican Johnny Isakson in November. Democratic incumbent Zell Miller chose not to seek re-election.
In the race for the soon-to-be-vacated seat of Georgia Court of Appeals, held by Judge Frank M. Eldridge, Debra Bernes is in the lead with 305,206 votes across the state — 30 percent support statewide.
In the runoff, Bernes will face candidate Mike Sheffield, who won 203,589 votes — 19.8 percent. Those eliminated Tuesday included Howard Mead, who finished with 19.7 percent, Thomas C. Rawlings, 11.8 percent; Lee Elizabeth Tarte Wallace, 11.6 percent; and William Ashley Hawkins, 7.6 percent.