Timofeeva stuns Haddad Maia in seven-year first at Australian Open
Playing at her first Grand Slam, the 20-year-old showed nerves of steel to down the Brazilian 7-6(7), 6-3 on Margaret Court Arena.
The victory added to her burgeoning reputation, having already beaten former champion Caroline Wozniacki.
She joins another young Russian, Mirra Andreeva, in the last 16 and will play unseeded Ukrainian Marta Kostyuk for a place in the quarter-finals.
At 170 in the world, Timofeeva is the lowest-ranked woman to get so far in Melbourne since Germany's Mona Barthel seven years ago.
"It feels like a fairytale, but with the support of this amazing crowd, I feel like anything is possible," she said. "This is all a new experience and I'm enjoying every second of it.
"Once I got to the main draw, I thought why not stay longer and enjoy this as long as possible and that really is the motivation."
Timofeeva was broken in her first service game by the Brazilian.
But she kept her cool to break back and take the first set to a tie-break, where she saved a set point before a Haddad Maia double fault at 8-7 cost her.
With her confidence building, the Russian broke Haddad Maia to love for a 2-0 lead in set two and never relinquished the lead as she stamped her authority on the match.
Timofeeva was equally impressive against 2018 champion Wozniacki, showing power and grit to haul herself back into that contest and ultimately prevail 1-6, 6-4, 6-1.