Sanders, a U.S. senator from Vermont, has won seven out of the last eight state-level Democratic nominating contests, trying to chip away at Clinton's big lead in the number of delegates needed to secure the party's nomination.
Wyoming's 14 Democratic delegates - fewer than any other state - are awarded proportionally based on support from individuals participating in the nominating contest.
Early estimates showed that while Sanders won the contest, both he and Clinton would likely receive seven delegates each in the close race, maintaining Clinton's lead overall.
Going into Wyoming, Clinton had more than half of the 2,383 delegates needed to win the nomination. Sanders trailed her by 250 pledged delegates, those awarded based on the results of the state nominating contests.
Clinton's lead widens when superdelegates, Democratic leaders who can decide whom to support at the party's July convention, are included in the tallies.
Clinton and Sanders both spent Saturday campaigning in New York, which holds its contest on April 19 and where a total of 291 delegates are up for grabs, more than 10 percent of the tally needed to win the party's nomination.
Sanders' wife, Jane Sanders, went onstage where he was speaking at a community college in Queens, a borough of New York City, to alert him to Saturday's victory.
"News bulletin - we just won Wyoming!" Sanders said to cheers.
Speaking to reporters after the event, Sanders said he believed he had enough momentum to secure the nomination.
"We are closing very fast," Sanders said.
Clinton, a former U.S. secretary of state, campaigned in the nearby borough of Brooklyn, where her campaign is based.
Clinton represented New York as a U.S. senator and considers the state her home turf. Recent polls have shown Clinton more than 10 points ahead in the state.
Tension between the two candidates flared earlier this week in a party race that has typically focused on policies and not personal attacks. The candidates dialed back their criticism of one another on Friday.
In Wyoming's Republican contest last month, U.S. Senator Ted Cruz of Texas beat New York billionaire Donald Trump, the party's front-runner. Cruz is trying to block Trump from receiving enough delegates to win the nomination outright, which would lead to a contested convention in July.
A new Reuters/Ipsos poll shows that a third of Trump's Republican supporters could consider abandoning the party's candidate if Trump is denied the nomination at a contested convention.