ATLANTA—The battle over electing new Democratic Party officials has revealed the growing populist energy within the party, which could fuel an electoral turnaround but also risks turning against the establishment.

Former Labor Secretary Tom Perez won a narrow second-ballot victory to become Democratic National Committee chairman over Minnesota Rep. Keith Ellison, disappointing the party’s progressive wing that latched on to Sen. Bernie Sanders during last year’s primary campaign. Despite Mr. Ellison’s defeat, the burgeoning...