An Associated Press analysis of exit poll data showed that Paul defeated Democrat Jack Conway on Tuesday night.
Paul attacked federal budget deficits, the economic stimulus and health care overhaul. Conway tried to portray Paul as extreme and out of touch.
The race turned personal with ads over religion and a scuffle where a liberal activist was stepped on by a Paul supporter.
It's Paul's first run for office, but he has a political pedigree: His father is Ron Paul, the Texas congressman and former presidential candidate cheered on by libertarians and others who embrace the tea party movement.