Coming in second place was Republican former Secretary of State Karen Handel with 19 percent.
The question was whether Ossoff, a 30-year-old owner of an investigative film company, could win more than 50 percent of the vote Tuesday.
Keeping Ossoff below 50 percent had been the GOP's primary goal, and they poured in over $4 million to attack him in the race's closing weeks, hitting him for allegedlyinflating his resume and tying him to national Democrats like House Minority Leader Nancy Pelosi.
IMAGE: Supporters of Sixth District Democratic nominee Jon Ossoff cheer at Election Night party in Sandy Springs, Georgia, April 18, 2017. Some Republicans have suggested Trump could personally campaign in Georgia now that it's a two-person race, while Democrats plan to keep up the pressure - after falling short in another recent House special election in Kansas.
But Ossoff, a documentary filmmaker and former congressional aide, told energized supporters before all the returns were in that he and Democrats "shattered expectations" with their performance. GOP Rep. Tom Cole of Oklahoma, an ally of House leadership, said congressional Republicans must start showing they can lead after the failure of their health care legislation, or risk voters snatching away their majorities. But the president called to congratulate her Wednesday morning, and Handel said she hoped he would come to campaign for her. Having allowed Democrats and progressive groups to almost steal a march on them in what should have been a relatively safe district, Republicans put up an Election Day response that barely snagged them a runoff in Georgia's 6th congressional district.
Republican U.S. Senator Lindsey Graham of SC said the race showed how the South was changing.
"This is already a remarkable victory", he later said in a statement after the results were announced.
He also recorded robocalls warning voters that Ossoff would derail the Republican agenda if elected.
A shock upset in the national spotlight, the argument goes, would deeply embarrass the president and could jumpstart efforts to retake control of the House of Representatives in next year's midterm elections. Donald Trump put out a frenzy of robocalls, and tried to make a scandal out of the fact Ossoff had temporarily moved 1.5 miles outside his district to be with his girlfriend in medical school.
Most election observers expected a late night of vote counting, with a race that could be decided by a single point or less.
"We take it very seriously, and I am proud to be the Republican going to the runoff", she added. But that a Democrat made it this far in Republican territory - he was the top vote-getter out of 18 mostly GOP candidates - is an impressive political feat.
Ossoff's early fundraising appeals encouraged voters to "Make Trump Furious".
Overall, turnout was high for a Special Election and, with a few more precincts left to count early Wednesday, it appeared Ossoff would end up with about the same percent Hillary Clinton got in the district in November.
Ossoff's failure to win the seat outright also highlights the ongoing problems with the Democratic Party.
The race quickly gained national attention, becoming the 11th most expensive election in House history, according to the Center for Responsive Politics.