Dugan received 56 percent of the vote to defeat veteran legislator Bill Hembree of Winston, who received 44 percent of the vote.
Dugan received 3,606 votes to Hembree's 2,857.
Hembree, a Douglasville insurance agent, won all 10 of the precincts in western Douglas and south Paulding counties, but could not overcome Dugan's advantage in Carroll County. Dugan received 75 percent of the vote in Carroll and won 25 of the county's 26 precincts.
Hembree, a longtime House of Representatives member, had been the top vote-getter out of four candidates Nov. 6 but did not get the majority needed to avoid the runoff.
Dugan will now face Libertarian candidate James Camp of Temple Jan. 8 for the District 30 seat. The Legislature is scheduled to begin its 2013 session Jan. 14.
The seat became vacant when Bill Hamrick resigned after being appointed to a Superior Court judgeship.