The Arizona wins handed enough delegates to Trump and Clinton to help them maintain their leads in the delegate count despite victories from their primary competitors -- Bernie Sanders and Ted Cruz -- for clinching their party's presidential nomination.
Sanders beat Clinton to post morale-boosting victories in Utah and Idaho while Trump's main rival Ted Cruz came out on top in Utah.
Trump's victory kept his momentum rolling despite concerted efforts by party establishment to thwart the 69-year-old real estate tycoon's presidential aspirations.
"Much bigger win than anticipated in Arizona. Thank you, I will never forget! Thank you, Arizona," Trump tweeted.
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Clinton,68, said she was "very proud" to have won Arizona and hit Republican candidates who she said were "literally inciting bigotry and violence."
With an impressive win in Arizona, Trump grabbed all the 58 delegates at stake in the state, thus, increasing his total to 739 delegates and further increasing the gap on delegate count with Cruz who has a delegate count of 425. To win the Republican presidential nominee, Trump needs 1,237 delegates.
He needs to win 52 per cent of the delegates in the rest of the Republican primaries. So far, Trump has won 19 States as against Cruz's victory in eight States so far.
Clinton currently has 1,670 delegates, which includes 1,159 won by her in various states and 467 super delegates who have pledged their support to her. Sanders has 886 delegates including 829 won in state primaries and caucuses.
The one with 2,382 delegates, would be declared the Democratic presidential nominee.
In Utah, Cruz won about 70 per cent of the vote while Ohio Governor John Kasich got 16 per cent and Trump came in third at 13 per cent.
"I wanted you all to be the first to know that today I am endorsing Ted Cruz for President," Bush, who was himself in the running for US President till recently, said.