Wilson, a nonprofit director from Decatur, finished first, and Morgan, a state representative from Austell, finished second in the six-person Democratic race Tuesday.
The Republican primary will also go to a runoff, but the nine-candidate contest was still too tight to call the top two finishers.
State rules that require a candidate to receive 50 percent plus one vote to advance to the general election.
The seat is being vacated after a single term by Superintendent John Barge, who was one of two unsuccessful Republican primary challengers to Gov. Nathan Deal.
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