WASHINGTON—Hillary Clinton has widened her lead to 25 percentage points in the race for the Democratic presidential nomination, a new Wall Street Journal/NBC News poll finds.

The former secretary of state leads Vermont Sen. Bernie Sanders 59% to 34%, a slightly larger margin than the 19-point gap in December.

The new national poll comes as surveys in Iowa and New Hampshire show the race tightening in the states that play host to the first two nominating contests. While losses there would be a setback for Mrs. Clinton, the new Journal/NBC News survey suggests that she would retain strong advantages in the later primaries. Mrs. Clinton owes her durable lead nationally to her strength with key subgroups in the Democratic primary electorate, including nonwhite, older and moderate-to-conservative primary voters.

The race looks much different in Iowa and New Hampshire. Aggregates of recent polls show the contests to be close in both states, with Mrs. Clinton edging Mr. Sanders in Iowa and the Vermont senator claiming a lead in neighboring New Hampshire.

Nationally, the race has changed little since October, Journal/NBC News polling finds. Support levels haven’t budged much for either of the two leading Democrats since Mrs. Clinton bounced back from a late-summer swoon, which had been driven by questions about her family’s charitable foundation and a federal probe into her use of a private email server as secretary of state.