“I’ve been organizing in New Mexico for close to 20 years, so it’s not like people weren’t familiar with me or what I stand for,” Ms. Haaland, 57, said in a telephone interview on Wednesday. “We have an extremely divisive president who disparages so many people. I felt like it was just time to stand up with a positive campaign.”

Another congressional race in New Mexico involving a Native American candidate was decided on Wednesday night, with the Republican, Yvette Herrell, a member of the Cherokee Nation, losing to Xochitl Torres Small, a Democrat and water rights lawyer, after absentee ballots were counted. Unlike many Native American politicians in other races, Ms. Herrell did not promote her indigenous heritage while campaigning.

In Kansas, Ms. Davids can add another first to the record books: She is the first openly lesbian candidate to be elected to Congress from the state. She attended Cornell Law School and was a White House fellow in the Obama administration before mounting a campaign highlighting her heritage, sexual orientation and martial-arts mettle.

“It’s 2018 and women, Native Americans, gay people, the unemployed and underemployed have to fight like hell to survive,” Ms. Davids, 38, said in one of her campaign ads. “It’s clear Trump and the Republicans in Washington don’t give a damn about anyone like me or anyone who doesn’t think like them.”

Jean Schroedel, a professor of political science at Claremont Graduate University in California, who studies Native American voting rights, said Ms. Davids’s campaign offered a blueprint for other candidates seeking to frame issues from a Native American perspective.

“Sharice not only won but just took out a rising star of the Republican Party,” Professor Schroedel said, referring to Ms. Davids’s opponent, Representative Kevin Yoder, a four-term incumbent who championed conservative causes. “Democrats have been targeting that seat for several cycles and she showed them how to get it done.”