"You sent a message that, in America, we stand together", she said.
Clinton's win in SC bodes well heading into Super Tuesday contests across the South, where several states are home to large populations of black voters.
Polls closed across the state at 7 p.m. It didn't take long before Clinton was announced as the projected victor.
In a statement, the Vermont senator vowed to fight on aggressively. "The last thing I am is a con man".
"This campaign is just beginning", he said. But the Florida senator warned Sunday on CBS' "Face the Nation that if Trump does win the nomination "it will split us and splinter us in a way that we may never be able to recover".
The Democratic front-runner won largely on the strength of her support from black voters - her so-called "firewall" that, in the end, held up.
Today's results also appeared to endorse the Clinton campaign's argument that although Sanders could compete in some early states, he would be unable to match her in less white, more diverse states in the South and the West.
He added: "Our grassroots political revolution is growing state by state, and we won't stop now".
News exit polls show Clinton beat Sanders by wide margins among women and African American voters, even outperforming Barack Obama's lead among black voters in 2008. Exit polls showed the former secretary amassing an astonishing 87 percent of the African-American vote in SC.
Not to worry, Clinton backers counseled, assuring the naysayers that SC would serve to restore order.
Facing tough odds to win in the state, Mr Sanders spent most of the past week in states that will vote in March.
Clinton's commanding win over Vermont U.S. Sen. Democrats looking for a candidate who cares about people like them or one who is honest and trustworthy overwhelmingly supported Sanders in Iowa, New Hampshire and Nevada. His pledge to fix a rigged economic system and to provide free college were met more with skepticism than enthusiasm.
Sanders bypassed SC, opting instead for rallies in Austin and Dallas he told the Rochester crowd were attended by 10,000 and 8,000 people.
Cruz called Super Tuesday "the most important day in this entire election cycle" and said that turnout is key.
The survey was conducted for The Associated Press and the television networks by Edison Research as Democratic voters left their polling places at 30 randomly selected sites in SC.
Thirty-five are awarded proportionally based on the results in each of the state's seven congressional districts, and 18 others are decided proportionally by the statewide outcome. Including superdelegates, Clinton now has at least 536 delegates, according to AP's count. Party Chairman Jaime Harrison will go with the primary victor, the party said.
But delegates matter a lot more than the popular vote in presidential primaries because the nominee from each party will be chosen by delegates at their national conventions this summer.