Omar and Talib are among 100 or more Muslims who ran for office in 2018, an unprecedented surge in political engagement for a community targeted by policies meant to keep them on the sidelines.
Her win goes into records, making her the second Muslim woman ever elected to the US Congress.
Omar will also be the first Congress member to wear a Muslim hijab, or head scarf.
In Minnesota, Omar, about 36 and a naturalised American citizen and state representative, follows another trailblazer: She will succeed US Congressman Keith Ellison, who in 2006 became the first Muslim elected to Congress and is stepping down to run for state attorney general.
Omar has forged a progressive political identity.
At least 14 killed in China highway pile-up
The accidents follow a dramatic bus crash on October 28 in southwestern China that killed 15 people. Local authorities have demanded that risky sections of expressways across the province be examined.
She shared: "We changed the course of history at a time we thought it was impossible".
The oldest of 14 children, Tlaib was born to a family of Palestinian immigrants in Detroit, where her father worked at a Ford Motor Co plant. I will be using my position in Congress so that no country, not one, should be able to get aid from the United States when they still promote that kind of injustice.
Omar said President Trump's "politics of fear" motivated her to get in the race.
A Muslim woman from Detroit has won the congressional seat long held by Democratic Rep. John Conyers, who stepped down amid sexual harassment claims by former staffers.
With no Republican challenger in the race, Tlaib's election on Tuesday became a formality.
The Minneapolis woman campaigned on policies embraced by the Democratic Party's most liberal wing: universal healthcare, free college tuition and robust public housing. She also has been mindful of the historic nature of her candidacy. "I can not wait to serve with you, inshallah", Omar, who also won her election, said on Twitter. "It just shows how incredibly wonderful our country can be", she said.