Republican Troy Balderson led Democrat Danny O'Connor by about 1,700 votes with all precincts reporting, although the OH secretary of state's office said a final result would be delayed until more than 8,000 provisional and absentee ballots were counted.
And in suburban Seattle, three Democrats vied in a jungle primary for the seat held by another retiring Republican, Rep. Dave Reichert.
In Ohio, the script for the special election was somewhat familiar: An experienced Trump loyalist, Balderson, was fighting a strong challenge from O'Connor, a fresh-faced Democrat, in a congressional district held by the Republican Party for more than three decades.
The 12th district has numerous hallmarks of areas that could be weak spots for Republicans this cycle - well-educated, relatively affluent suburbs that may have soured on Trump and are looking to register their frustration through their midterm vote.
And even as they celebrated victory, one of those groups warned it can't be duplicated across the map in three months if some Republicans don't up their efforts. In doing so, he ignored the pleas of the Republican Governors Association to stay out of the race.
The election is seen as a key indicator ahead of November's mid-terms.
In the Republican primary for Kansas governor, Trump on Monday endorsed Kobach, the Kansas secretary of state known for his crusade for restrictive voting laws, over incumbent Colyer.
O'Connor refused to concede on Tuesday night and urged supporters on Twitter to make donations for what "could be a long and expensive recount".
Mr Trump himself campaigned at Mr Balderson's side just 72 hours before Election Day, a weekend appearance to help energise his loyalists in a district the president carried by 11 percentage points. "He said, 'No, I didn't, '" Kasich said of Balderson on ABC's "This Week".
Mike Flynn, a hospital unit co-ordinator from suburban New Albany northeast of Columbus, voted for Balderson as a show of support for Tiberi. "It's really kind of shocking because this should be just a slam dunk and it's not". Even in voter interactions, Balderson left much to be desired. Also, she met with President Donald Trump during a recent trip to Washington, D.C.
Republicans have pumped money into the race in hopes of avoiding another special election embarrassment.
"While we won tonight, this remains a very tough political environment and moving forward, we can not expect to win tough races when our candidate is being outraised", Corry Bliss, the head of the big-spending Congressional Leadership Fund, warned in a Tuesday night statement.
O'Connor dominated Balderson on the local airwaves.
"We're not stopping now, " Democrat Danny O'Connor told cheering supporters. The Congressional Leadership Fund's ads have similarly latched O'Connor to Pelosi.
"Winning any of them would be icing on their cake".
Democrats, meanwhile, have been attacking Balderson by casting his support of tax cuts as threats to Social Security and Medicare.
Trump made his preference clear for Kobach.
To win, Balderson will need to unite Republicans who love the president and those who prefer the governor. "Strong on Crime, Border & Military", the president tweeted on the eve of the election. "VOTE TUESDAY!" Trump tweeted.
In a swing State that Mr. Trump won by eight points in 2016, Mr. Balderson's 10-point lead from June has evaporated.
Peoples reported from NY.
O'Connor said in a speech Tuesday that he's ready to go on to November, where he and Balderson will run again.
Former Democratic Party legislative leader Gretchen Whitmer will face off in the MI gubernatorial race against Trump ally Bill Schuette. Bernie Sanders 2016 alums to his campaign.