The issue of immigration loomed large in the south-western state, the biggest prize in the latest round of contests, according to the BBC.
Polls showed that Mr. Trump's anti-immigration message resonated with the state's conservative voters.
During a victory speech in Seattle, Mrs. Clinton addressed the terrorist attacks in Brussels on Tuesday, pushing back against the Republican candidates' response to the bombings.
Earlier on Tuesday, Mr. Trump reiterated his plan to ban Muslims from travelling to U.S. and suggested that the U.S. should torture terrorism suspects.
"We live in a complex and dangerous world," Mrs. Clinton said. "And we need a commander-in-chief that can provide leadership that is strong, smart and above all steady in taking on these threats.
The last thing we need are leaders who incite more fear," she said, alluding to Mr. Trump.
