The Democratic wave that rose on Election Day in Virginia last month delivered a final crash on the sand Tuesday when a Democratic challenger defeated a Republican incumbent by a single vote, leaving the Virginia House of Delegates evenly split between the two parties.

The victory by Shelly Simonds, a school board member in Newport News, was a civics lesson in every-vote-counts as she won 11,608 to 11,607 in a recount conducted by local election officials.

Ms. Simonds’s win means a 50-50 split in the State House, where Republicans had clung to a one-seat majority after losing 15 seats last month in a night of Democratic victories up and down the ballot, which were widely seen as a rebuke to President Trump. Republicans have controlled the House for 17 years.

“I just can’t believe it, but it sounds like it’s pretty solid,” an excited Ms. Simonds, speaking from a bar with the sounds of celebration in the background, told reporters on a conference call. She said she was in awe of the recount process, an example of what she called good government, in which there were no arguments between Democrats and Republican observers. “It was a beautiful thing to see democracy in action.”