Exit polls showed one of the largest racial divides in a primary yet, with about 90 per cent of black voters favouring the Illinois senator but only about a quarter of white voters choosing him.
That extended a pattern of black support that carried him to victory in earlier southern primary elections in South Carolina, Alabama, Georgia and Louisiana.
On Tuesday, racial remarks about Obama by a prominent Clinton supporter had sparked a harsh exchange between the two camps.
"If Obama was a white man, he would not be in this position," Geraldine Ferraro, the Democratic vice-presidential candidate in 1984, told a California newspaper.
"And if he was a woman 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," Ferraro said.
Clinton said she did not agree with the comments and called them "regrettable", but the Obama camp accused her of double standards for refusing to rebuke Ferraro and dismiss her for the remarks.
Obama's top foreign policy adviser resigned last week after telling a British newspaper Clinton was "a monster".
"I don't think Geraldine Ferraro's comments have any place in our politics or in the Democratic party. They are divisive," Obama said in an interview with a Pennsylvania newspaper.
"I would expect that the same way those comments don't have a place in my campaign they shouldn't have a place in Senator Clinton's either," he said.
Maggie Williams, a Clinton campaign manager, accused Obama's campaign of "false, personal and politically calculated attacks on the eve of a primary".
Obama won the Democratic contest in the western state of Wyoming over the weekend, although the sparsely populated state had only 12 delegates on offer.
Obama has 1,579 delegates while Clinton, senator for New York, has 1,473, according to the latest AP tally before taking into account the 33 at stake in Mississippi.
Either candidate must win 2,025 delegates to clinch the nomination, however the contest could go on to the Democratic party's convention in August.