Earlier, Halep breezed through her fourth round match on with a 7-5, 6-1 victory over China's Wang Qiang.
Although Halep's own performance was far from faultless, particularly in the first set, the Romanian triumphed 7-5 6-1 and will now face Petra Martic in the last eight.
This content is restricted to site members. Wozniacki had a chance to get the No. 1 back but she needed to win the Indian Wells title to do it.
"I think she should have been ranked as she left", Halep added.
After recently taking back the world No. 1 ranking from Caroline Wozniacki, Halep is off to a fantastic start at the tournament.
Part of Halep's preparation for Indian Wells included hitting balls with Wang. She asked Darren Cahill's advice and her coach suggested her to work longer points and reduce the error count.
"In the beginning it was really tough because I was really nervous going on the big stages against big players", she said.
"It was really important, because he just told me what I have to do. I knew that I had to change something, but I didn't realize what it was exactly", she said.
The writing was on the wall for Wang when she also lost the first three games of set two. She is on the verge of her second career singles title at Indian Wells. "So I know a little bit how she's playing, but I will focus on myself like always".
She used her protected ranking to play at Wimbledon in the same year. It was the first time Venus has beaten Serena since 2014 in Montreal.
Williams, who is the oldest female player in the draw at 37, rallied in the second set against Sevastova to book her spot in the quarter-finals.
She next faces either wild card Danielle Collins or world number 27 Carla Suarez Navarro of Spain.
No.5 seed Karolina Pliskova ended the fairytale week of the ninth 16-year-old player to make R16 at Indian Well.The Czech outclassed 6-1 7-6 (2) Amanda Anisimova, the youngest player to record a Top 10 win since 2005 when Nicole Vaidisova defeated then No.9 Nadia Petrova to win the title in Bangkok.