Is there a rising progressive tide in the Democratic Party? Liberals like to claim that there is. But beyond the recent elections of two vocal populists—Senator Elizabeth Warren of Massachusetts and New York Mayor Bill de Blasio—there hasn't been a whole lot of evidence to point to. Indeed, in two of the most hyped challenges to centrist Democratic officeholders—the recent primaries of New York Governor Andrew Cuomo and Chicago Mayor Rahm Emanuel—the left has come up short. And things aren't looking much better for Vermont Senator Bernie Sanders in his left-wing challenge to Hillary Clinton.

On Tuesday, though, progressives scored a victory. The Democratic primary for Philadelphia mayor pitted a crusading left-winger against a charter-school advocate backed by suburban hedge-fund magnates. This time, the left-winger, a former city councilman named Jim Kenney, actually won. Given the city's overwhelmingly Democratic tilt, the primary is likely to decide the election.

Kenney ran on a de Blasio-esque platform of establishing universal pre-K, raising the minimum wage to $15 per hour, and ending stop-and-frisk police tactics. (Kenney, a 57-year-old Irish-American, also epitomizes the classiness and tact for which Philadelphia sports fans are famed: In December, he called New Jersey Governor Chris Christie "fat assed" and "a creep" for sitting in the Dallas Cowboys' box at an Eagles game.) On Monday, de Blasio endorsed Kenney, saying the two shared a "progressive vision." Kenney’s campaign was outspent many times over by supporters of his chief rival, Anthony Hardy Williams, a state senator who was backed by a $7 million super PAC. But on Tuesday night, Kenney took 56 percent of the vote.

The Kenney-Williams divide typifies the current split within the Democratic Party between those who style themselves "pro-business" and those who emphasize remedying income inequality. It's a conflict that's also currently playing out on Capitol Hill, where President Obama is in an increasingly acrimonious dispute with the majority of congressional Democrats over a Republican-backed trade-authority measure. The split has echoes of the 1990s battles between Bill Clinton's Democratic Leadership Council and the party base led by Jesse Jackson.

Education is a major fault line in the current Democratic divide—in Chicago, Emanuel's school policies were a principal driver of the dissatisfaction that forced him into a runoff last month. De Blasio has also been in high-profile fights with New York charter-school advocates, while Obama's stance in favor of education reform has dismayed the teachers’ unions that are a major Democratic Party constituency.

Williams, Kenney's rival, was the author of a state law that created a voucher-like system giving companies tax credits in exchange for student scholarships. The super PAC backing him was bankrolled by three financiers who support free-market education reform. Yet in addition to backing Kenney, Philadelphia voters on Tuesday also approved an advisory ballot question seeking to return public schools to local control. Kati Sipp, director of Pennsylvania Working Families, a union-backed liberal coalition, declared the primary "a big win for public education," adding, "Money men tried to buy this election, but they failed."

Liberal activists say Kenney's election is further proof that the center of the Democratic Party is indeed moving leftward—a trend that Clinton, even without a serious primary challenger, will have to grapple with in 2016. Also Tuesday, the city council in Los Angeles voted to raise that city's minimum wage to $15 per hour. "The energy in the Democratic Party is on the left," Anna Greenberg, Kenney's pollster, told me. "It's coming from the urban centers, and that's where Democratic votes come from."