Mitt Romney squeezed past Rick Santorum to win Ohio's presidential primary, capturing the biggest Super Tuesday prize but raising enough doubts to quash hopes of quickly ending the Republicans' bruising nominating fight.

A week after the former Massachusetts governor seemed to take command of the presidential race with victories in Arizona and, more significantly, his native state of Michigan, the contest was pitched into renewed upheaval.

With more than 99% of the Ohio votes counted, Romney was clinging to a narrow lead of about 12,000 votes.

The former Massachusetts governor won five other states: Virginia, Vermont, Massachusetts, Idaho and Alaska, piling up nominating delegates in the process.

"We're going to get more before this night is over," Romney told cheering supporters in Boston. "We're on our way."

His mood, however, appeared less celebratory than resigned to at least several more weeks of hard campaigning, which he and many in the party had desperately hoped to avoid.

Santorum won North Dakota, Oklahoma and Tennessee. The latter two denied Romney the Southern breakthrough he had sought to show his appeal among religious voters and cultural conservatives, underscoring their stubborn resistance toward his candidacy.

Santorum, speaking before the results in Ohio were known, struck a proud and defiant note.

"We've won races all across the country against the odds," the former Pennsylvania senator said at a late-night rally in Steubenville, Ohio. "When they thought, OK, he's finally finished, we keep coming back."

Former House Speaker Newt Gingrich carried Georgia, home of the district he represented for years in Congress. He too said victory proved the naysayers wrong, and expressed his determination to fight on.

"I want you to know, in the morning, we are going to Alabama, we're going on to Mississippi, we're going on to Kansas — and that's just this week," Gingrich told cheering supporters in Atlanta, referring to the next sets of contests.

In all, voters in 10 states were casting ballots in Super Tuesday contests. But while Georgia dispensed the most delegates, the greatest attention was focused on Ohio, a November battleground where Romney and Santorum devoted the bulk of their time and resources.

Both candidates focused on the economy in a Rust Belt state that hurt long before the rest of the country sank into deep recession, then emerged to a fitful recovery.

Santorum touted his roots across the border in a Pennsylvania steel town, saying he would seek to strengthen the economy by restoring America's manufacturing might. Romney unveiled a new slogan — "more jobs, less debt, smaller government" — and jabbed at Santorum's digression into subjects like contraception and the separation of church and state.

"During this campaign there has been discussion about all sorts of issues," Romney said in Canton. "I keep bringing it back to more jobs, less debt and smaller government. That's what my campaign is about."

Ohio is vital to GOP hopes of winning the White House: No Republican has even been elected president without carrying the state. Romney's struggle to fend off Santorum — despite considerable advantages — seemed certain to seed further doubts about his ability to win over working-class and blue-collar voters who are vital to Republican success in the battleground states of the Midwest.

The results flashed other caution signs. Romney trailed Santorum and Gingrich, respectively, among the most conservatives voters in Ohio and Georgia, according to exit polls. He also showed continued weakness among evangelical Christians, perhaps because of concerns about his Mormon faith.

While those voters — who represent the base of the party — are likely to rally behind the eventual winner, the resistance has kept Romney from wrapping up the nominating fight as quickly as he would like.

The fourth candidate in the race, Rep. Ron Paul of Texas, was hoping for his first victory in the one remaining caucus state, Alaska. (Voters in Wyoming were also caucusing, but they will not finish for some time.) Paul campaigned hard in North Dakota and appeared there election night, but came up unavailing.