Democrats had hoped a new election in the 28th District would provide an opportunity for an even split in the chamber, which is now on track to be controlled by a 51-49 GOP majority.
Democrats cited state election officials who said 147 voters received the wrong ballot before Republican Bob Thomas beat Democrat Joshua Cole by only 73 votes.
It is the second defeat in as many days for Democrats. On Thursday, election officials broke a tie vote in another House district by drawing names from a bowl, and picking the Republican.