"It's a long road to 1600 Pennsylvania Avenue, and it runs right through the heart of Pennsylvania," she told supporters in Philadelphia.
"I'm in this race to fight for you ... You know you can count on me to stand up strong for you every single day in the White House."
Clinton commended Obama and his campaign, saying the two are in many ways "on this journey together."
Clinton's big-state victory follows her wins in Ohio, New York, Texas and California.
Her campaign said that should raise questions about whether Obama, who leads Clinton in the overall Democratic race, can beat presumptive Republican nominee John McCain in November.
"The tide is turning," Clinton told cheering supporters. Chelsea Clinton's eyes welled with tears as she watched her mother speak.
Clinton will pick up a majority of the state's 158 delegates.
"Yesterday, we had record turnout in Pennsylvania," she said on CNN's "American Morning" Wednesday. "I won that double-digit victory that everybody on TV said I had to win, and the voters of Pennsylvania clearly made their views known -- that they think I would be the best president and the better candidate to go against Sen. McCain.
"It was inspiring and so exciting because this has been a six-week campaign, one on one. Voters got to look at both of us, consider both of us. I was outspent three to one, and the results were just enormously exciting and gratifying to me."
But the win still leaves Obama ahead in the race to the Democrats' August convention in Denver, and he is likely to hold that lead unless "the wheels come off his wagon," said CNN analyst David Gergen, a former adviser to both Republican and Democratic candidates.
"He came up short, but it doesn't look like the wheels came off," Gergen said. "That's going to be her problem. I don't see her way to the nomination. The wheels aren't coming off the wagon unless there is some new, big revelation."
According to CNN's latest count, Obama leads in the delegate count -- 1,694 to 1,556.
He also leads in the popular vote and the number of states won so far this primary season.
CNN analyst and Clinton supporter Paul Begala said Clinton still scored "an extraordinary victory" in Pennsylvania.
Obama congratulated Clinton on her win and looked ahead to the May 6 contests in North Carolina and Indiana.
"There were a lot of folks who didn't think we could make this a race when it started," he said in Evansville, Indiana.
"But we worked hard ... And now, six weeks later, we closed the gap. We rallied people of every age and race and background to the cause. And whether they were inspired for the first time or for the first time in a long time, we registered a record number of voters, and it is those new voters who will lead our party to victory in November."
Obama drew more than 90 percent of the vote among Pennsylvania's black voters, who are heavily concentrated around Philadelphia.
African-Americans made up about 14 percent of Tuesday's vote.
But whites made up about 80 percent -- and voted 60-40 for Clinton. Her supporters turned out heavily in Pittsburgh and the counties of western Pennsylvania, and she was racking up similarly lopsided margins in the state's industrial northeast, the exit polls found.
Obama also scored big with new Democrats in Pennsylvania.
One out of every seven Democratic party voters was not registered as a Democrat at the beginning of the year, and 60 percent of them cast their ballot for Obama, according to the exit polls.
Clinton fared better with voters who made up their mind in the last week, the exit polls showed.
Fifty-eight percent of those voters said they chose the New York senator. That includes voters who made up their mind in the aftermath of last week's heated Democratic debate.
Clinton also got the support of older voters, with 61 percent of those age 65 or older backing her, according to the polls.
In recent weeks, Clinton fended off calls to drop out of the race as the increasingly bruising primary fight raised worries from within the party that the daily cycle of charge-and-countercharge could hurt the Democrats' chances in the general election.
Neither candidate is expected to win the 2,025 delegates needed to clinch the nomination by the end of the primary season in June.
The superdelegates -- party leaders and officials -- then could decide the nomination.
CNN's Paul Steinhauser and Chris Welch contributed to this report.