PHILADELPHIA — Hillary Clinton gained a firm grip on the mantle of presumptive presidential nominee for the Democratic Party Tuesday, a position she failed to secure eight years ago, after steaming through the “Acela primary’’ with wins in Maryland, Delaware, Connecticut, and the big prize of the night, Pennsylvania.

But rival Bernie Sanders’ victory in Rhode Island serves as a persistent reminder that Clinton has yet to persuade an increasingly fractured party to coalesce around her and bolstered the Vermont senator’s rationale for staying in the contest.

Seeking to unify the party behind her, Clinton made an overture to its liberal wing in her victory remarks from the Philadelphia Convention Center Tuesday night.

“I applaud Senator Sanders and his millions of supporters for challenging us to get unaccountable money out of our politics and give greater emphasis to closing the gap of inequality,’’ Clinton said. “And I know that together we will get that done.’’

She added: “Whether you support Senator Sanders or you support me, there’s much more that unites us than divides us.’’

The Democratic primary season has already stretched well beyond the time frame any political strategists would have guessed a year ago when Clinton led in national and early state polls with commanding margins. The race instead turned into a slog, where Clinton failed at multiple junctures to soundly shut down Sanders’ insurgent presidential bid.

And even as Sanders’ path to the nomination has become fainter, tens of thousands of people still pack his rallies, visit his website to donate money, and monitor Twitter to respond to any perceived slight. That core of support from young voters and independents wary of the political establishment propelled Sanders to victory in 17 of 38 contests held before the five states that voted Tuesday.

And many are staying with him. Twenty-five percent of Sanders supporters won’t vote for Clinton in November, ­according to a McClatchy-Marist poll conducted this month.

Clinton delivered her Pennsylvania victory speech in a ballroom just four miles north of the Wells Fargo Center, which hosts events for the Democratic Party’s convention in three months. The July convention was on her mind.

“With your help we’re going to come back to Philadelphia for the Democratic National Convention with the most votes and the most pledged delegates,’’ Clinton said.

Just under 75 percent of the Democratic party’s delegates have been awarded. All of the states in the Democratic contest award delegates proportionally, so Sanders would have to not only win the remaining states but win with much larger margins than he has to date to catch up to Clinton.

Sanders traveled to Huntington, W.V., on election night, holding a rally in a state with 29 delegates that votes on May 10. He showed no signs of quitting the race.

“The reason we are generating this enthusiasm is because we are doing something very unusual in contemporary American politics: We are telling the truth,’’ said Sanders to a cheering crowd that he estimated at 6,000. “Truth is not always pleasant. It is not always something you are happy to hear. If we go forward as a nation, we can’t sweep the hard realities of our lives under the rug.’’

Sanders ticked off statistics about McDowell County in West Virginia. It’s a place, he said, where the average male can expect to live to age 63.

“What being poor is about in America is you die at a significantly lower age than people who have money,’’ he said.

In an interview on MSNBC Tuesday morning, Sanders floated Senator Elizabeth Warren as a potential running mate, describing her as “a real champion in standing up for working families, taking on Wall Street.’’

But a more realistic question is how he wants to influence the Democratic Party, and what he will want in return for his support and valuable list of campaign contributors.

His loss in Pennsylvania, however, is particularly devastating. Sanders’ team had — even just a week ago — predicted that the Vermont senator would prevail in the state on his message of combatting income inequality, exposing a rigged system, and opposing trade deals that have devastated parts of the state.

But the whopping 16-point loss in New York April 19 blunted any momentum that he’d hoped to ride to victory here. In an interview broadcast on “Meet the Press’’ Sunday, Sanders acknowledged that he has a “narrow path’’ to the nomination.

On Tuesday night, though, he suggested that he’d stay in the race right to the convention, making his case to so-called superdelegates who overwhelmingly back Clinton.

“Almost every national poll and every state poll have us defeating Trump and that margin for us is significantly larger than that of secretary Clinton,’’ Sanders said.

“The reason that we are doing so much better against Republican candidates is not only are we winning the majority of Democratic votes, but we were winning independent votes and some Republican votes as well,’’ he said.

“That is a point that I hope the delegates to the Democratic convention fully understand,’’ he said.

The argument ignores the fact that Sanders’ national poll numbers haven’t been weighed down with the tens of millions of dollars of negative ads that are baked into Clinton’s.

“I’ve wanted to yell that from the rooftops,’’ said Gus Bickford, a superdelegate from Massachusetts who is supporting Clinton. “There is a significant difference when you look at arace that is actually happening and what could be.’’

Clinton, he said, has been subject to attacks for two decades, “for the very reason that she and her husband are very talented.’’

In recent days Clinton has repeatedly pointed out that she has opened a larger lead over Sanders than Barack Obama did over her in 2008. She expressed an enthusiasm to turn to the general election.

“I am winning,’’ Clinton said Monday night on an MSNBC forum in Philadelphia. “And I’m winning because of what I stand for and what I’ve done.’’

The Sanders team showed no movement toward unity. On Tuesday afternoon, Sanders campaign manager Jeff Weaver sent out a fund-raising e-mail highlighting the at-times friendly relationship between Clinton and Republican front-runner Donald Trump.

It featured a now iconic photo of the Clintons standing in formal attire and grinning next to the newly married Trumps.

Even if Sanders does stay in the race through the June 7 primary in California, as he has repeatedly pledged to do, there’s some evidence that his core of support is finding some measure of acceptance in the likely outcome.

A viral video titled “Bernie math’’ posted on CollegeHumor.com, a website geared toward young people who make up Sanders’ base, pokes fun at the candidate’s narrowing path and the fever of his support.

It features a white male college student struggling over a math assignment to show that Sanders is actually winning the race “like the Internet says he is.’’

“I’m usually pretty good at math, but this just doesn’t make any sense to me,’’ the student says to a friend who offers to help. He reads off Clinton’s delegate count, and then reads Sanders’ smaller number.

“I just compared the two numbers and saw which one was bigger,’’ the student says. His friend grows angry, accusing him of being a Clinton supporter.

“I’m not saying anything about the candidates themselves,’’ the frustrated student says. “I’m saying that if you look at the numbers, Hillary Clinton’s delegate count is bigger.’’

As of Tuesday afternoon it had been viewed nearly a million times.

Annie Linskey can be reached at annie.linskey@globe.com. Follow her on Twitter @annielinskey.