With 99% of ballots counted, Mrs. Clinton had a lead in the Bluegrass state of 46.7% to 46.3% - just 1,813 votes.
But Mr. Sanders was projected the winner of Oregon's primary on Tuesday, by 53% to 47%.
The Vermont senator has built on his commanding victory last week in neighboring West Virginia, Sky News reported.
But Mrs. Clinton, a former Secretary of State, remains on track to clinch the Democratic presidential nomination in early June.
Mr. Sanders has vowed to continue fighting until July's party convention, a distraction for his rival's campaign.
The Clinton camp is eager to focus on presumptive Republican nominee Donald Trump ahead of November's election.
Mr. Trump won Oregon's primary by 64.2% on Tuesday, a victory which was a foregone conclusion since he is now running unopposed.
Tuesday's contests took place amid an ugly dispute among the Democrats following chaotic scenes at the party's Nevada convention on Saturday.
Sanders supporters threw chairs, heckled speakers and harassed the state party chair with death threats.
They accused the party leadership of rigging the results of the convention to award more delegates to Mrs. Clinton, who won the state's caucuses in February.
Heading into Tuesday, Mrs. Clinton had the backing of 2,240 delegates, including 524 so-called superdelegates who can change their allegiance at any time before the party's convention.