Pune-born Sawant, 40, was declared elected after her nearest rival 16-year incumbent Richard Conlin conceded defeat as her lead grew to 1,640 votes -- less than one per cent of the total votes.
The victory of the first socialist was celebrated with an impressive gathering in Seattle.
Her call to take Boeing -the biggest private employer of the region, which is threatening to move jobs out of the state - into public ownership was welcomed with a standing ovation.
"Our campaign is not an isolated event, it's a bellwether for what's going to happen in the future," she added.
Sawant is an economics teacher at Seattle Central Community College and a member of the American Federation of Teachers Local 1789.
She was an activist in the Occupy Wall Street movement.
In 2012 Sawant won a 29 per cent with over 20,000 votes as a Socialist Alternative candidate against Democratic WA State House Speaker Frank Chopp - the strongest vote for an independent left-wing candidate in the US in 2012, and the highest vote for a socialist in decades.
During the campaign she did not accept any corporate funding.
Born to Vasundhara and H T Ramanujam in Pune in 1973, Sawant grew up in Mumbai where she later studied computer science and graduated with a BS from the University of Mumbai in 1994.
Sawant married her husband Vivek, an engineer at Microsoft, and moved to the United States. After moving to the United States Sawant decided to abandon the computer engineering field.
