A confident Trump declared that it was "impossible" for his rivals to catch him. "We don't have much of a race anymore," he said during a victory rally in the lobby of the Manhattan tower bearing his name.
Clinton's triumph padded her delegate lead over rival Bernie Sanders and strengthened her claim to the Democratic nomination that eluded her eight years ago. Clinton's campaign is eager to turn toward the general election and heal wounds with Sanders' enthusiastic supporters.
Trump needed a strong showing to keep alive his chances of clinching the GOP nomination before the party's July convention and to quiet critics who say the long primary season has exposed big deficiencies in his campaign effort.
Trump leads the GOP race with 756 delegates, ahead of Cruz with 559 and Kasich with 144. Securing the GOP nomination requires 1,237.
Among Democrats, Clinton now has 1,862 delegates to Sanders' 1,161. Those totals include both pledged delegates from primaries and caucuses and superdelegates. It takes 2,383 to win the Democratic nomination.