With 72 percent of precincts reporting in Kentucky, Clinton led Obama 65 percent to 31 percent, CNN reported.
Exit polls had indicated Clinton won among men, 62 percent to 32 percent, and among women, 67 percent to 27 percent.
Democrats in Kentucky were also choosing who will challenge Republican Senate Minority Leader Mitch McConnell, The Hill reported.
In Oregon, Democrats were choosing who will take on Republican Sen. Gordon Smith.
Meanwhile, Republicans sought a candidate they could run to replace Rep. Darlene Hooley, D-Ore., who is retiring.
A SurveyUSA poll of the contest between state Rep. Jeff Merkley and activist Steve Novick for the right to face Smith showed Novick held a slim 3-percentage point lead.