With no Republicans on the ticket in Tuesday's nominating primary, Ms Pressley is all but certain to succeed Mr Capuano in Washington in November's congressional elections.
If elected in November, she will be the first black woman to represent the state in Congress.
"It seems like change is on the way", said Pressley to raucous applause at her election night party. Though in both primaries a woman of color defeated a white man who had been in Congress for decades, the MA race does not fit the narrative of a progressive political newcomer unseating an Establishment Democrat.
Pressley has bristled at the notion that race was a defining issue in her campaign.
Pressley's upset Tuesday night marked the latest victory for progressives against Democratic establishment candidates.
Pressley is backed by Alexandria Ocasio-Cortez, the leftist socialist who defeated Crowley in NY on a message of pushing to "Abolish ICE".More news: Kansai Airport flooded by Typhoon Jebi, 5,000 stranded
"Everyone knows she gave me my roots to my wings", Pressley told the Herald.
But, she added, "When the challenges we are confronted with are this big, this deep, and growing, I can't and I won't wait my turn".
As in Ocasio-Cortez's race, Pressley was a progressive woman of color challenging a white male lawmaker.
Pressley tapped into growing cries within the Democratic Party for newer, more diverse leadership.
Polls and political analysts predict the state's nine House of Representatives seats will remain in Democratic hands, along with the seat held by U.S. Senator Elizabeth Warren, a leading liberal voice often cited as a possible 2020 White House contender.
Both contended that Baker's support among voters was soft and that his administration had failed to make significant strides in many areas, particularly the problems plaguing the Boston-area transit system known as the 'T'.
Republican Gov. Charlie Baker won his party's nomination for a second term, defeating Scott Lively, a conservative minister and staunch supporter of Trump who frequently called Baker - a frequent critic of the president - a RINO, or Republican in Name Only.