An Ossoff win would not tip the balance of power in the Republican-controlled House but could weaken Trump's already shaky hold on his party there by encouraging those in competitive districts to distance themselves from him.
The Republican scramble has been intense, with rivals accusing Handel of being a political opportunist and the conservative Club for Growth spending six figures on ads to defeat her. He even mocked Ossoff's choice of residence - outside the district.
The Ossoff threat clearly caught Trump's attention.
"We have an fantastic chance here, an extraordinary moment for Georgia", Ossoff told campaign volunteers as they headed out for a final round of door-knocking on Monday afternoon.
Trump did not perform as well as other Republicans last November in the Georgia district, an affluent, well-educated swath filled with the kind of voters Democrats need if they hope to reclaim a House majority next year.
Karen Handel, Georgia's former secretary of state, has led the Republican field.
The first-place finish by Ossoff, a 30-year-old former congressional aide and filmmaker, was greatly aided by millions of dollars in donations from restive Democrats and by the presence on the ballot of almost a dozen Republicans, which split the party's vote.
The district, which encompasses a swath of well-heeled suburbs north of Atlanta, has elected Republicans to the House since the late 1970s, but Trump carried it by only 1 percentage point in the November presidential election.
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In a runoff, Ossoff could find it hard to sustain the momentum he witnessed this past week in a traditionally Republican district that has been in GOP hands since 1979.
It still wasn't enough for voters like Matt West, a 45-year-old financial planner from Roswell.
A political action committee backed by current Speaker Paul Ryan funneled more than $2 million into attacks on Ossoff, mostly tying him to national Democrats such as House Minority Leader Nancy Pelosi. I've been living with Alicia, my girlfriend of 12 years, down by Emory University where she's a full-time medical student.
Mr. Trump's perceived weakness in the district, along with its changing demographics, convinced Democrats to pour millions of dollars into the race.
Whatever the outcome, the race highlights Republican candidate's challenge in dealing with the president: He still engenders intense loyalty among his core supporters, but alienates many independents and some Republicans.
Handel's showing was due to more than name recognition from her long tenure in state politics.
Tuesday's primary lumps all 18 candidates -Republicans, Democrats and independents - on one ballot in a race that is testing both parties' strategies for the 2018 midterm elections with Trump in the White House. They predict conservative voters would be energized in a Republican vs. Democrat scenario. A special election last week in Kansas resulted in a close call for the GOP in what is typically a solid Republican district.
Associated Press reporter Catherine Lucey in Washington and Kathleen Foody in Alpharetta, Georgia, contributed.