After most of the votes were counted on Monday night, NBC and the New York Times called the result -- a narrow victory for Biden, who is up against Sanders for the chance to challenge President Donald Trump in November.
They said that former vice president Biden had won 37.9 percent of the vote, with the leftist Sanders close behind with 36.4 percent.
The result came as millions of Americans were due to troop to polling stations in three more states on Tuesday, with anxiety running high over the fast-spreading coronavirus that has killed more than 80 people in the US so far.
As Arizona, Florida, and Illinois prepare for the primaries, there was confusion over whether polling stations will be safe during the pandemic.
Voting has been postponed in Ohio, where officials ordered polling stations closed, making it the latest and largest state to upend the voting schedule due to the outbreak.
Tuesday may be a make-or-break moment for Sanders, who will face mounting pressure to quit if he does not score a major upset.