Breaking a 12 contest losing streak, Clinton won Ohio with 141 delegates at stake and won Rhode Island, with 21 delegates up for grabs. In Ohio, Clinton won women and won white men, with huge margins among women and men without a college degree, according to exit poll results.
Obama, meanwhile, racked up a win in Vermont's Democratic primary -- a win that was expected by both candidates and credited to that state's sizeable population of liberal and Independent voters who have typically gone for the Illinois senator.
In Vermont, Obama beat Clinton among senior citizens as well as among white women, two of her core groups. His focus on "change" prevailed over "experience" by nearly a 40-point margin.
But it was Clinton's hold on low-income, low-education Democrats and women -- key demographic groups in Ohio that could help her win in Pennsylvania over a month from now.
Clinton had the most at stake coming into the race, facing pressure to cede the nomination battle if she didn't win both Texas and Ohio, with a combined 370 delegates up for grabs.
Even former President Bill Clinton said she must win both states to stay in the race, although a new ABC News/Washington Post poll shows Democrats by a 2-1 margin think the former first lady should fight on even if she only wins one or the other.
Some influential Democrats suggested Clinton should drop out of the race if she wasn't ahead after Tuesday's votes.
"We have to have a positive campaign after Tuesday. Whoever has the most delegates after Tuesday, a clear lead, should be, in my judgment, the nominee," New Mexico Governor Bill Richardson, a Democratic superdelegate himself, said on CBS's Face The Nation Sunday.
Outside a Houston elementary school, the voting site for a heavily Hispanic area, Clinton indicated Tuesday morning she planned to stay in the race.
"I don't pay attention to what people are saying," Clinton said. "This is a long process as some of you have heard me say before," she told reporters. "My husband didn't get the nomination wrapped up until June. That has been the tradition — that it usually lasted longer."
Asked about the ABC News/Washington Post poll which seems to support Clinton's perspective, she replied, "Never underestimate the intelligence of the voter."
Latinos turned out in big numbers in the Texas Democratic primary, accounting for a record 30 percent of voters, up from 24 percent in 2004, according to preliminary exit poll results.
Latinos went 63-35 percent for Clinton over Obama. Clinton also won white women in Texas by 19 points while white men split evenly between Clinton and Obama. The Illinois senator won 85 percent of black voters in Texas, who accounted for 19 percent of Democratic primary voters in the Lone Star State.
Many Texans took advantage of early voting rules; early voting is expected to account for 50 percent of the total Democratic primary votes, according to the Texas Secretary of State's office.
But earlier Tuesday Clinton expressed dismay at the peculiar voting rules in Texas, where Democratic delegates are allocated through a combination of the results from primary votes and caucuses. Texas apportions delegates in a complex system that may yield Obama more delegates from expected wins in Texas' big cities, while giving Clinton less delegates for expected wins in Latino areas along the border.