Ted Cruz has won all 14 delegates in contention at a state party convention in Wyoming.
The delegates were chosen by Republican members rather than ordinary voters.
Ted Cruz’s rival Donald Trump – who did not actively campaign in the state – remains the Republican front-runner overall.
However, Donald Trump could fall short of the number of delegates needed to secure the Republican nomination for the November presidential election.
That would mean a contested convention where voting for candidates starts again from scratch.
Donald Trump is concentrating on New York, which holds a key primary on April 19.
A number of senior Republican leaders have backed Ted Cruz, a Conservative Texas senator, fearing that Donald Trump’s controversial comments make him a weak candidate in the November election.
The result from the Wyoming contest brings Ted Cruz’s tally from 545 to 559 delegates. Donald Trump has 743.
In his victory speech on April 16, Ted Cruz said: “If you don’t want to see Donald Trump as the nominee, if you don’t want to hand the general (election) to Hillary Clinton, which is what a Trump nomination does, then I ask you to please support the men and women on this slate.”
In the Democratic race, Hillary Clinton is still ahead of her only remaining rival, Vermont Senator Bernie Sanders.