The victory puts Williams back in the semi-finals at Indian Wells for the first time in 17 years.
She skipped the tournament from 2002 to 2015 in the aftermath of her controversial withdrawal from the semis in 2001 where she was due to meet sister Serena.
Spectators vented their displeasure with the withdrawal during the final, booing Serena and jeering Venus and father Richard Williams when the pair arrived to watch the match. Richard Williams alleged he had heard racist taunts.
"This was my first breakout tournament when I was 16 so to come back and get closer to hopefully a title, it's like a dream come true," said Venus, who was taught the game by her father on the courts of Compton, California.
"I definitely feel the crowd behind me if I'm getting behind and when I get match point I feel the love," she said.
"So I love it, I'm happy. This is home."
Friday's semi-final will pit the 37-year-old against 20-year-old Kastakina, who needed less than an hour to defeat former world No. 1 Kerber earlier on Thursday.
Kastakina won five of her six break point opportunities in a dominant performance. The Russian has been toppling big names all tournament long, also defeating U.S. Open champion Sloane Stephens and world No. 2 Caroline Wozniacki on the way to the semi-finals.
Williams, the tournament's No. 8 seed, has split her only two career meetings with the 20th-seeded Kastakina.
The winner will face either world No. 1 Simona Halep or 20-year-old Naomi Osaka of Japan, who are set to play their semi-final on Friday.
(Reporting by Rory Carroll in Los Angeles; Editing by Peter Rutherford)
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