“I'm excited,” he said Wednesday. “As I understand, I kind of made history. I'm the first candidate to run against candidate Burnett and actually come out ahead.”
Ray was not immediately able to be reached for comment Tuesday.
The winner of the runoff will face Democratic candidate Deborah Davis in the November general election.
Burnett said despite Tuesday's numbers, he has no plans to end his campaign.
Ray took just less than 45 percent of the vote, and Burnett secured a little more than 37 percent of the vote, according to complete and unofficial election results.
Early voting for the runoff is July 23 to 27.