He remains ahead in the overall contest in terms of delegates but is trying to regain momentum lost last week when Mrs Clinton won Ohio and tied in Texas.
Wyoming sends 12 delegates to August's Democratic convention, making it one of the smallest prizes in the race.
The next test for the Democrats is the Mississippi primary on Tuesday.
After netting seven of Wyoming's delegates to Mrs Clinton's five, Mr Obama now has a total of 1,578 against 1,468 for his rival, according to the Associated Press.
It takes 2,025 to secure the party's nomination.
The Republican party has already chosen John McCain as its candidate for the November presidential election.
Iraq strategy
Mr Obama told supporters in Wyoming on Friday that he would end the war in Iraq in 2009.
HILLARY CLINTON: 1,468
Delegates needed to secure nomination: 2,025. 
But a former adviser told the BBC earlier this week that the Illinois senator's exit date was a "best-case scenario" that he would revisit if he became president.
Campaigning in Mississippi, Mrs Clinton also called for an end to the Iraq involvement.
"He [Mr Obama] has attacked me continuously for having no hard exit date, and now we learn he doesn't have one, in fact he doesn't have a plan at all," she said.
Both candidates have reported massive fund-raising totals for February, with Mr Obama bringing in $55m (£28m) and Mrs Clinton $35m (£17m).
Running mates?
Amid the intense rivalry, Mr Obama has played down the possibility he could run as Mrs Clinton's vice-president.
"You won't see me as a vice presidential candidate - you know, I'm running for president," he told CBS affiliate KTVQ-TV on Friday.
"We have won twice as many states as Senator Clinton, and have a higher popular vote, and I think we can maintain our delegate count."
Mrs Clinton has previously hinted she would consider sharing the ticket, with Mr Obama as her vice-presidential candidate.
After Tuesday's primary in Mississippi, in which 33 Democratic delegates will be awarded, the next major battle will be the Pennsylvania primary on 22 April, with 158 delegates up for grabs.
Debate on whether to hold fresh ballots in Florida and Michigan also continues.
Both states were told their delegates would not be seated at the party's August national convention - meaning they cannot vote on who should be the Democratic presidential candidate - after they breached party rules by holding primary elections before 5 February.
Aides to Mrs Clinton have indicated they would be open to new elections being held, saying they believe her prospects would be good.
RACHMAD YULIADI NASIR
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