With 60 percent of the votes counted, Horsford tallied 51 percent of the vote compared with 42 percent for Republican Danny Tarkanian, the son of the popular former University of Nevada, Las Vegas, basketball Coach Jerry Tarkanian.
Nevada was considered a swing state prior to the election and neither party was a clear winner Tuesday.
President Obama received the state's six electoral votes with 53 percent of the vote to Mitt Romney's 46 percent with 93 percent of the votes counted.
The four House races were split between the Democrats and Republicans. Along with Horsford, the Democrats elected Dina Titus in District 1. Republicans Mark Amodei and Joe Heck won in Districts 2 and 3 respectively.
The U.S. Senate race between Republican Sen. Dean Heller and Democrat Shelley Berkeley was separated by 1 percentage point late Tuesday with 92 percent of the votes tabulated.