SAN JUAN COUNTY, Utah — In this county of desert and sagebrush, Wilfred Jones has spent a lifetime angered by what his people are missing. Running water, for one. Electricity, for another. But worst of all, in his view, is that the Navajo people here lack adequate political representation.

So Mr. Jones sued, and in late December, after a federal judge ruled that San Juan County’s longtime practice of packing Navajo voters into one voting district violated the United States Constitution, the county was ordered to draw new district lines for local elections.

The move could allow Navajo people to win two of three county commission seats for the first time, overturning more than a century of political domination by white residents. And the shift here is part of an escalating battle over Native American enfranchisement, one that comes amid a larger wave of voting rights movements spreading across the country.

“It’s a historic moment for us,” said Mr. Jones, during a drive on the county’s roller coaster dirt roads. “We look at what happened with the Deep South,” he went on, “how they accomplished what they have. We can do the same thing.”