Hillary Clinton and Bernie Sanders battled to a split decision in Tuesday’s Democratic contests, but the former secretary of state maintained her commanding lead in the chase for delegates by winning the primary in Arizona, the day’s biggest prize.

Mr. Sanders notched victories in both the Utah and Idaho caucuses, claiming his first states since he scored an upset in Michigan two weeks ago.

Tuesday’s results still left Mr. Sanders behind his Democratic rival in the delegate count, as Arizona offered more delegates than Idaho and Utah combined.

Mrs. Clinton celebrated her victory at a rally in Seattle, where she was campaigning ahead of Saturday’s Washington state caucuses. She looked past Mr. Sanders entirely and sharply criticized Republicans, particularly front-runner Donald Trump, who won the GOP primary in Arizona, and said voters understand that the race under way isn’t just a choice between candidates.

“This is a contest between fundamentally different views of our country, our values and our future,” she said.