With 100 percent of precincts reporting, Balderson had a 1,754-vote lead over O'Connor, with more than 202,000 votes cast.
The close race in the OH special election became a referendum on Trump's leadership and a last chance to gauge Democratic strength ahead of November's midterm elections.
The best barometer for November's midterm elections came in OH, where the contest in a congressional district near Columbus that Republicans have held for three decades was too close to call.
The five-way Democratic primary featured labor lawyer Brent Welder, who campaigned recently with self-described democratic socialists Vermont Sen.
For Republicans, it was costly: The Congressional Leadership Fund super PAC and the National Republican Congressional Committee, the House GOP's campaign arm, poured a combined total of more than $5 million into the race, compared to just $1 million from the Democratic Congressional Campaign Committee.
In what should have been a slam dunk for the Republican, Tuesday's special election for a central OH congressional district was locked in a tight battle late Tuesday.
Trump claimed victory in one race, nevertheless.
Democrats could also celebrate their showing in a district that has gone Republican for decades.
President Donald Trump carried the district by 11 points against former Secretary of State Hillary Clinton in the 2016 presidential contest, but Tiberi's retirement threw the congressional race wide open. Republican Troy Balderson has 101,566 votes, and Democrat Danny O'Connor has 99,800.
The election is seen as a key indicator ahead of November's mid-terms.
Balderson and O'Connor will face off again in November to fill the next two-year term. There were at least 3,367 provisional ballots left to be reviewed. Once they are tallied, an automatic recount would be triggered if the margin of results is within 0.5 percent. It won't be clear until all of the votes are counted and certified whether O'Connor will be able to demand a recount. Democrat Danny O'Connor, trailing in the latest count, vowed: "We're not stopping now". Polls in the final week showed the contest in all but a dead heat. Mr. O'Connor insisted he would not support her return to the role of speaker if Democrats regain control of the House.
Kobach, the Kansas secretary of state, built a national reputation as a conservative agitator for both tough immigration policies and strict voter identification laws.
While the marquee race in Kansas this year is for governor, voters also were picking candidates to contest two House seats that Democrats are hoping to flip in November. However, former Detroit health director Abdul El-Sayed lost his bid to become the country's first Muslim governor to a more moderate Democrat, former state Senate leader Gretchen Whitmer.
It appears that all the Republican candidates so far called as winners have been endorsed by Mr Trump. Kansas does not hold runoff elections so the victor in the primary will move on to November.
Kobach and Colyer were virtually tied atop a seven-candidate field early Wednesday with most of the outstanding results from Johnson County in the Kansas City suburbs, which has almost 23 percent of the state's voters.