The opposition will take the seats of Swan, Pearce and Hasluck from the Liberal Party, according to ABC projections, as vote counting continues late on Saturday. It is also ahead in the usually safe Liberal-held seat of Tangney.
High-profile independent candidate Kate Chaney is also waging a forceful challenge against her Liberal rival in the traditional Liberal stronghold of Curtin.
The significant swing in the nation's west could be enough to help Labor govern in its own right, although a minority government remains a possibility.
An enormous roar greeted the vote updates at the Belmont Sport and Recreation Centre, in the electorate of Swan, where Labor volunteers and supporters gathered.
Ms Mascarenhas was greeted by even louder cheers on arrival.
"I know you guys have been working hard so take a seat," she said.
"I am humbled that the people of Swan have elected me."
Ms Mascarenhas said Labor would boost local manufacturing, create an integrity commission and fix the aged care sector.
"And finally, something very close to my heart, strong action on climate change. We have an opportunity for Australia to become a renewable energy superpower. WA can be a part of that, mining can be a part of that. We can become a lithium valley. There are so many opportunities," she said.
Labor campaigned heavily in WA, with leader Anthony Albanese making four visits to the state since pandemic border restrictions were relaxed in March. The state has been a stronghold for Liberal federal governments ever since former Labor leader, Perth-born Kim Beazley, retired from politics.
Ms Chaney, a so-called teal independent, said she would negotiate with the major parties should she win the contest in Curtin, and if her support was needed for a minority government to be formed.
"I would make a decision made on the issues, not on the tribe," she told Sky News on Saturday.
"What I hear from voters in Curtin is that they're quite disillusioned with both sides and they really care about issues like integrity and climate and think that those issues are actually more important than who the prime minister is for the next three years.
"If my support is needed to form a minority government, I would negotiate with both parties and whether that is a formal or informal deal that can be part of the negotiation if it happens."
In NSW, Liberal MP Trent Zimmerman conceded the seat of North Sydney, paving the way for independent Kylea Tink to head to the House of Representatives.
Zoe Daniel (seat of Goldstein in Victoria) and Allegra Spender (Wentworth, NSW) are among several other independents on track to oust their Liberal rivals.
