In the race for delegates, CBS News projects that Obama will win 19 delegates in Mississippi and Clinton will win 14.
Overall, Obama has 1,593 delegates to Clinton's 1,471. (Click here for the latest state-by-state tally.)
With nearly all precincts reporting in Mississippi, Obama led Clinton 61 percent to 37 percent. (Click here for complete Mississippi results.)
According to CBS News exit polls, the economy was the most important issue on the minds of Democratic voters in Mississippi. This has been the case throughout the primaries.
More than half of Democratic voters cited it as their number one issue, and almost nine in ten said they believe the U.S. economy is in bad shape.
Also, according to exit polls, a majority of Democratic voters in Mississippi thought favorably of the two Democrats running together in the general election campaign. Fifty-six percent said that they think if Clinton is the eventual Democratic nominee, she should pick Obama as her vice presidential running mate. And 54 percent say that if Obama is the eventual Democratic nominee, he should pick Clinton as his vice presidential running mate.
On CBS News' The Early Show, co-anchor Harry Smith asked Obama if he would put Clinton on his "short list" of potential running mates.
"I think Senator Clinton is a very able and smart and tough person, and I think she'd be on anybody's short list to consider," Obama said. "Because she's obviously got a terrific constituency and has proven to be a terrific and tenacious campaigner."
Democratic voters do have strong opinions about who should be at the top of the ticket, according to the exit poll. Among Clinton voters, just 27 percent would be satisfied if Obama were the nominee. Among Obama voters, 42 percent would be satisfied if the nomination went to Clinton, while 57 percent would be dissatisfied. (Click here to see the Democratic exit poll.)
"There appears to be some hardening among the supporters for both these candidates," said CBSNews.com senior political editor Vaughn Ververs. "Voters supporting each are more likely now to say they would be unsatisfied with the other, indicating that some of the increased rhetoric is taking a toll on what has been a remarkably united and energized party to this point. With six weeks before the next contest in Pennsylvania, that's something Democrats will watch carefully."
While savoring his primary victory, Obama also predicted a united Democratic party in the general election.
"Obviously I think I would be the better nominee," he said in an interview on CNN. "But I have been careful to say that I think Senator Clinton is a capable person and that should she win the nomination, obviously I would support her."
But in a race growing more contentious, he took a swipe at the way his rival's campaign has conducted itself.
"We've been very measured in terms of how we talk about Senator Clinton," he said. "I've been careful to say that I think Senator Clinton is a capable person and that should she win the nomination, obviously, I would support her. I'm not sure we've been getting that same approach from the Clinton campaign."
The exit polls showed a racially divided electorate. While nine in 10 blacks lined up behind Obama, seven in 10 whites supported Clinton.
Black voters accounted for roughly half the ballots cast in Mississippi, according to the exit polls. Obama's support among them extends a pattern that carried to him to victory in other contests across the Deep South, including South Carolina, Georgia and Alabama.
The volatile issue of race has been a constant presence in the historic Democratic campaign, and it resurfaced during the day in the form of, the 1984 Democratic vice presidential candidate and a Clinton supporter.
"If Obama was a white man, he would not be in this position. And if he was a woman (of any color) he would not be in this position. He happens to be very lucky to be who he is. And the country is caught up in the concept," she said in an interview with the Daily Breeze of Torrance, Calif., that was published last Friday.
Clinton expressed disagreement with Ferraro's comments, and said, "It's regrettable that any of our supporters - on both sides, because we both have this experience - say things that kind of veer off into the personal."
Obama called Ferraro's remarks "patently absurd."
Both Obama and Clinton campaigned in Mississippi, although the former first lady seemed to go out of her way to say she did not expect to win.
"Some people have said 'Well Mississippi is very much a state that will most likely be in favor of Senator Obama.' I said 'Well, that's fine,' but I want people in Mississippi to know I'm for you," she said in Hattiesburg before flying to Pennsylvania.
After the results came in, Clinton's campaign released a statement congratulating Obama.
"We congratulate Senator Obama for his win in Mississippi and thank our supporters and volunteers there for their support, hard work, and long hours. Now we look forward to campaigning in Pennsylvania and around the country as this campaign continues," said campaign manager Maggie Williams in the statement.
Obama made a stop Tuesday in Greenville before heading to Pennsylvania, too.
"I've been praying for you," a man called out.
"I believe in prayer," Obama replied.
The Illinois senator also spent all of Monday in Mississippi, drawing enthusiastic crowds in Columbus and Jackson, the capital.
After losing 12 straight primaries and caucuses, Clinton rebounded last week with primary victories in Ohio, Texas and Rhode Island. Obama won the Vermont primary and led in the Texas caucuses so far -- the party has said official results from the caucuses won't be available until March 29.
But the damage was deeper than mere numbers - costing him a chance to rally uncommitted party leaders to his side, and depriving him of an opportunity to drive the former first lady from the race.
Reinvigorated, Clinton immediately began talking about the possibility of having Obama as her running mate.
Obama ridiculed the idea, saying, "I don't know how somebody who is in second place is offering the vice presidency to the person who is first place."
Other than Pennsylvania, there are primaries remaining in Indiana, North Carolina, West Virginia, Kentucky, Oregon, Puerto Rico, Montana and South Dakota.
Adding to the uncertainty in the lengthening race between Obama and Clinton, Democrats from Florida and Michigan are pressing for their delegations to be seated at the summer convention.
Both states were stripped of their delegates by the Democratic National Committee after they held early primaries in defiance of party rules. But efforts are under way to find a compromise that would satisfy party leaders in both states as well as the candidates, possibly through primaries-by-mail.
The Republican primary in Mississippi provided no suspense sincehas already amassed enough delegates to win his party's nomination. McCain won about 80 percent of the Republican vote in the primary.
The Arizona senator was in New York attending an evening fundraiser that was expected to raise $1 million.