Cook ranks the race between Republican Katie Arrington and Democrat Joe Cunningham among 10 districts that could flip between the parties if an expected "blue wave", favoring Democrats in the midterm congressional elections, swells into a "blue tsunami".
However, if Balderson keeps the victory, it will be short-lived - the seat will go up for election again in November for the general midterm election.
President Trump campaigned for Balderson, a 56-year-old state senator, this past weekend in an effort to energize the GOP base, but some Republicans anxious that the president's appearance could have had an adverse effect by motivating voters who don't like Trump to come out for O'Connor.
Trump was quick to claim victory, tweeting "When I made a decision to go to OH for Troy Balderson, he was down in early voting 64 to 36". Heading into the vote, the Republican candidate in a long-held conservative district had a slim one-point lead over the Democrat contender.
Kansas is a deep-red state - Trump won there by 20 percentage points in 2016 - and any Republican would be favored in the gubernatorial election in November.
He held a rally in the district on Saturday to energise the party's base ahead of the special election that was triggered by the retirement of sitting Republican congressman Pat Tiberi.
Republican outside groups spent more than $5 million combined to salvage Balderson's prospects in the race after he was vastly out-raised by O'Connor.
On Tuesday night, he appeared to take credit for the Culberson win amid the congratulations. He called the race "very close".
Meanwhile, more than 700 miles to the west, Kansas Republicans were fighting among themselves in the battle for governor, where Secretary of State Kris Kobach was trying to unseat Gov. Jeff Colyer.
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Bournemouth will be hoping to wrap up the signing of Colombian defensive midfielder Jefferson Lerma for a club-record fee. Speaking on Friday, new Blues manager Maurizio Sarri said he was unsure whether Courtois would stay.
Trump didn't seem anxious about Kobach's prospects.
Michigan State Attorney General Bill Schuette won the Republican nomination for governor on Tuesday night, defeating three other candidates working to fill the seat to be vacated by conservative Gov. Rick Snyder.
The Republican victory would mean Democrats will still need a net pickup of 23 seats to win the House this fall. Democrats weren't even supposed to be competitive here. All 435 House seats, 35 of 100 Senate seats and 36 of 50 governors' offices are up for grabs in November.
O'Connor dominated Balderson on the local airwaves.
The five-way Democratic primary features labor lawyer Brent Welder, who campaigned recently with self-described democratic socialists Vermont Sen. Bernie Sanders and NY congressional nominee Alexandria Ocasio-Cortez, who catapulted to fame when she defeated the No. 4 House Democrat in a June primary.
But political observers said the fact the race was so close in a district that Democrats have not held since Ronald Reagan was president was notable.
Also in the race: Native American attorney Sharice Davids and former school teacher Tom Niermann. Two vulnerable Senate Democrats, Missouri's Claire McCaskill, and Michigan's Debbie Stabenow are facing challenges in their states.