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.
Two Muslim women have been elected to the House of Representatives for the first time.
Omar, the first Somali-American Muslim to be elected to the Minnesota legislature or any elected office in the United States, is also part of a historic wave of women looking to clinch higher.
Tlaib's win comes after the 2016 election of Trump spurred a record number of women to put their names on the ballot.
Her parents were Palestinian immigrants from the West Bank and Jerusalem. She will be the first hijab-wearing member of Congress. "I couldn't sit on the sidelines", she said. She spent four years of her childhood in a refugee camp in Kenya. She eventually settled in Minneapolis. That may force her to resign from Detroit City Council to do so. She supports free college education, housing for all, and criminal justice reform.
US Elections: Referendum on Trump’s presidency? - Rabobank
New Jersey and Pennsylvania are important pieces of the puzzle for Democrats in their hopes of taking back the House. To win a majority, the Democrats need to flip 24 Republicans seats and hold onto the 194 seats they already hold.
Omar was leading with more than 80% of the vote when the Associated Press called the race for Minnesota's 5th Congressional District at 8:33 p.m.
During her campaign, Omar focused on single-payer health care, gun control and immigration.
The pair's election to the US House of Representatives comes amid widespread negative feeling against American-Muslims by their compatriots.
Haaland, a member of the Pueblo of Laguna tribe, is a well-known community activist in her solidly Democratic district, working tirelessly to encourage Native Americans - who make up two percent of the United States population - to vote.
In February, Omar spoke openly about what she saw as the president's prejudice against Muslims, saying there is no debate about "whether Trump is a racist".
Some analysts who have closely followed Washington politics say Tuesday night's election outcomes are unsurprising.