With all votes counted, Texas Senator Cruz won 66.3 percent of the ballots in the western state, far ahead of his nearest rival, Florida Senator Marco Rubio, who earned 19.5 percent of the vote, US media reported.
Trump, the bombastic real estate magnate leading in polls and in delegates to the Republican national convention, came in third with a measly 7.2 percent of the vote.
The additional 12 delegates from Missouri could give
The additional delegates bring Trump slightly closer to the 1,237 needed to secure the Republican presidential nomination.
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Trump now has 758 delegates, Cruz has 538, Marco Rubio has 173 and John Kasich has 145.
Clinton and Trump are leading in the race to secure their respective party nominations ahead of election day on November 8.
The next primaries are set to take place on April 19 in New York where Clinton and Trump are both leading in opinion polls.
A Quinnipiac University survey showed Clinton -- who represented New York for two terms in the Senate -- with 53 per cent support along likely primary voters to 40 per cent for Sanders.
On the Republican camp, Trump has a significant lead over his rivals at 55 per cent of likely voters, to 20 per cent for Kasich and 19 per cent for Cruz, the Quinnipiac poll showed.