Paul had 59 percent of the vote - with returns counted from 29 percent of the precincts - to 37 percent for Secretary of State Trey Grayson, who had been recruited to run by the state's dominant Republican, U.S. Senate Minority Leader Mitch McConnell.
In a Democratic primary that commanded far less national attention, Attorney General Jack Conway led Lt. Gov. Daniel Mongiardo, 49 percent to 39 percent.
On the busiest primary night of the year so far, Democratic Sens. Arlen Specter in Pennsylvania and Blanche Lincoln in Arkansas struggled uncertainly for nomination to new terms.
In a fourth race with national implications, Republican Tim Burns and Democrat Mark Critz vied to fill out the final few months in the term of the late Rep. John Murtha in Pennsylvania. Each political party invested nearly $1 million in that contest and said the race to succeed the longtime Democratic lawmaker was something of a bellwether for the fall.
In Oregon, Democratic Sen. Ron Wyden faced little opposition for nomination to a third full term.
Voters in Pennsylvania and Oregon also selected gubernatorial candidates.
In Kentucky, Grayson had the support of McConnell as well as other establishment figures. But Paul countered with endorsements - and the political energy that flowed along with them - from tea party activists, former Alaska Gov. Sarah Palin and Sen. Jim DeMint of South Carolina, a conservative eager to push his party rightward in advance of the broader fall campaign.
Eager to avoid long-term fallout from a bruising primary, GOP leaders set a unity breakfast for Saturday.
