Joe Biden trounced Bernie Sanders in Florida, the largest state at stake on Tuesday, and was cruising to victory in Illinois, according to network projections.
The centrist Mr Biden also tops the polls over the leftist Mr Sanders in the other state voting on Tuesday - Arizona.
A win in Arizona, added to his Florida and Illinois victories, could give Biden an all-but insurmountable lead over Mr Sanders in the race to decide who will top the Democratic ticket against President Donald Trump in November.
Edison Research polls found a majority of voters in all three states trusted Mr Biden more than Mr Sanders, a US senator from Vermont, to handle a major crisis.

Former Vice President Joe Biden and Senator Bernie Sanders greet each other before participating in a Democratic presidential primary debate. Source: AAP
The polls also found about half of voters in Illinois were “very concerned” about the potential effects of the COVID-19 outbreak, which caused Ohio to cancel its planned nominating contest on Tuesday.
Gloved poll workers and hand sanitiser dispensers met voters in the three states amid a health crisis that has upended the campaign and shut down much of American life as in other parts of the world.
Mr Sanders, 78, who trailed Mr Biden in opinion polls in all three states, could face renewed pressure to end his bid if he loses badly on Tuesday. Many Democrats do not want a repeat of 2016, when they believe his long, bitter primary battle with Hillary Clinton played a role in her upset loss to Mr Trump, 73.
Because of the coronavirus, Edison Research, which normally conducts exit polls, spoke by telephone to early voters and others who planned to vote.
The polls found seven of 10 voters in Florida and six of 10 in Illinois and Arizona trusted Mr Biden more than Mr Sanders in a crisis.
They also found seven of 10 voters in all three states believed Mr Biden had the best chance of beating Mr Trump, a crucial factor in a Democratic race where electability has been the top priority for many voters.
There were signs coronavirus concerns had hurt turnout on Tuesday, though officials also noted that early voting and voting by mail had surged. That could still boost overall turnout above the levels in the Democratic primary in 2016, the last year Americans voted for president.
Ohio also had been scheduled to vote on Tuesday, but Governor Mike DeWine said public health concerns made in-person voting too dangerous and postponed the election to 2 June.
“Our goal is that no one will have to choose between their constitutional rights and risking their health,” Mr DeWine told a news conference on Tuesday, adding that going ahead with the vote would have been “a real, real disaster.”