COLUMBIA, S.C. — Hillary Clinton won a decisive victory in the Democratic primary in South Carolina on Saturday, giving her campaign a significant boost in the race against insurgent Sen. Bernie Sanders and demonstrating her advantage with the minority voters crucial to winning the party's nomination for president.

In a victory speech to supporters, Clinton insisted that she was not assuming the nomination was already hers, promising she was “not taking anything and not taking anyone for granted.”

But she was clearly looking beyond the primary contest toward a general election that appears likely to be waged against Donald Trump. She did not mention the New York businessman by name, but left no doubt who she was referring to as she declared:

“Despite what you hear, we don't need to make America great again. America has never stopped being great,” she said. “But we do need to make America whole again. Instead of building walls, we need to be tearing down barriers.”

Sanders conceded the South Carolina contest in a statement issued only minutes after the state's polls closed, but pledged that he would continue to campaign.

“This campaign is just beginning,” Sanders said. “We won't stop now.”

The fact that Sanders felt the need to say that, however, pointed to both the magnitude and importance of Clinton's victory here.

The win put Clinton's campaign back on firmer footing after a bumpy start to the race. South Carolina is often a bellwether of support among black voters. African-Americans were projected to account for well over half of those who turned out Saturday, and Clinton won roughly 8 in 10 of their votes, according to the exit polling conducted for the major television networks and The Associated Press.

Clinton now heads with confidence into the Super Tuesday contests this week. The highest-stakes states in those contests are also ones with large black Democratic electorates, and polls show Clinton with a commanding lead in most of them.

“To me, there is no state more important than South Carolina,” said Cornell Belcher, who was a pollster for President Barack Obama when he won the state in 2008. “If, in South Carolina, Bernie Sanders shows an inability to compete for African-American voters, he cannot be the nominee.”

In interviews last week, some black voters confessed they had little familiarity with the Vermont senator, despite enthusiasm for him among some black celebrities and activists.

Rapper Killer Mike campaigned for Sanders in barbershops. Film director Spike Lee cut a campaign advertisement for him. The Sanders campaign also produced a gripping video in which Erica Garner, whose father died after being held in a chokehold by New York police, talked about why Sanders is most qualified to confront racial injustice.

Yet the efforts were largely overshadowed by those of Clinton, who had won the loyalty of a larger and more influential coalition of African-American leaders, including U.S. Rep. James Clyburn, D-S.C.

Sanders has taken a very different approach to reaching out to minority voters than Clinton, who is more comfortable with the politics of identity and speaks eloquently and forcefully on the ills of white privilege. Sanders has kept his focus on the economy, arguing it is rigged for the benefit of the 1 percent, and a fundamental restructuring would improve the fortunes of blacks.

His more radical policy proposals, including free public college, a $15 minimum wage and a European-style system of government-provided health care have connected with some younger blacks frustrated with the pace of change under the Obama administration. And Sanders' railing against the criminal justice system's mistreatment of blacks has also earned him support, particularly among voters who are uncomfortable with Clinton's history of promoting harsh punishments for offenders when she was first lady.

As Sanders struggles to win over minority voters, the delegate math is looking increasingly in Clinton's favor. Polls show Clinton with a commanding lead in high-delegate states Texas, Georgia and Virginia, as well as in several Southern states.

Even Massachusetts, a neighbor to Sanders' home state of Vermont, is looking to be a toss-up.

Yet Clinton's momentum is also running into the impressive Sanders fundraising machine, which is built on more than a million small donors whose enthusiasm and devotion to the Vermonter's candidacy outstrips what Clinton has been able to muster.

Even a weak showing on Super Tuesday is unlikely to change that.

“Hillary is moving with a lot of wind at her back,” said Ed Rendell, former Pennsylvania governor and chairman of the Democratic National Committee. “But it isn't over for Bernie because Bernie will have the money to contest her all the way to California, if he so desires.” The California election is still three months away.

Evan Halper reported from Washington and Chris Megerian from Charleston. Tribune Newspapers' Kurtis Lee contributed from Columbia.

evan.halper@tribpub.com