Mrs Clinton’s win gave the former US secretary of state’s White House campaign a huge boost and puts her in a strong position as the race heads towards crucial multi-state contests tomorrow.
She said on Twitter: “To South Carolina, to the volunteers at the heart of our campaign, to the supporters who power it: thank you.”
At a campaign victory party in state capital Columbia, supporters broke into raucous cheers as the race was called in her favour. She told her victory rally that “tomorrow this campaign goes national” as she and Mr Sanders compete for the Super Tuesday states.
To cheers, she said: “When we stand together there is no barrier too big to break.”
Mr Sanders, expecting defeat, left the state before voting was finished and turned his attention to some of the states that vote in this week’s delegate-rich contests.
He vowed to fight on aggressively, saying: “This campaign is just beginning. Our grass-roots political revolution is growing state by state and we won’t stop now.”
Black voters powered Mrs Clinton to victory in South Carolina, with eight in ten voting for her. She also won over most women and voters 30 and older, according to early exit polls.
Her victory came at the end of a day that saw Republican candidates firing insults at each other at rallies in states voting tomorrow.
Donald Trump, working to build an insurmountable lead campaigning in Arkansas with former rival New Jersey governor Chris Christie, called Florida senator Marco Rubio a “light little nothing”.
Texas senator Ted Cruz asked parents in Atlanta, Georgia, if they would be pleased if their children spouted profanities like brash billionaire Mr Trump. And Mr Rubio mocked Mr Trump as a “con artist” with “the worst spray tan in America”.
Mrs Clinton made a stop in Alabama, a Super Tuesday state, before returning to Columbia for a victory party.
Meanwhile, Mr Sanders drew 10,000 people to a rally in Austin, a liberal bastion in conservative Texas, the biggest Super Tuesday prize.
He has energised young people and liberals with his impassioned calls for breaking up Wall Street banks and making tuition free at public colleges and universities.
But the senator from Vermont – a state where only about 1 per cent of the population is black – lacks Mrs Clinton’s deep ties to the African-American community.
Mrs Clinton’s sweeping victory suggested South Carolina voters had put aside any lingering tensions from her heated contest with Barack Obama, who won the state in the primary race in 2008.
Her husband, former president Bill Clinton, made statements during that campaign that were seen by some as questioning the legitimacy of the black presidential contender.
This time around though, Mr Clinton was well-received as he travelled the state on his wife’s behalf.
She focused on issues with particular resonance in the black community, including gun violence, and held an emotional event with black mothers whose children died in shootings.