In other third round matches, Canadian No. 1 Milos Raonic beat Portugal's Joao Sousa 7-5, 4-6, 6-2 and Sam Querrey of the United States rallied to outlast Yuki Bhambri 6-7 (4/7), 6-4, 6-4.
Halep advances to the quarters where she will face unseeded Petra Martic of Croatia who beat Czech Marketa Vondrousova 6-3, 7-6 (7/4).
She next faces either wild card Danielle Collins or world number 27 Carla Suarez Navarro of Spain.
"I wasn't missing that much", she said.
"It was a quick turnaround from last night when it feels like, 'Hey, this is a final to you're only in the fourth round, '" Williams said on court.
The 26-year-old is yet to win a Grand Slam title but underlined her resilience in testing circumstances to recover from a break deficit in the final set and set up a meeting with either world No 5 Karolina Pliskova or Japan's Naomi Osaka. Halep needs to be at her best moving forward. "From my side, it was like a chess game because we've got a bit time during the game, during the ball was flying, so you can, like, in one second to think where to put the ball, how to put the ball... That's why I'm trying just to go in to watch every time I can".
Kohlschreiber will next play the unseeded Pierre-Hugues Herbert, who won his third round match when fellow Frenchman Gael Monfils retired with a back injury.
The Romanian, who is the only remaining defending champion after Caroline Wozniacki's exit on Tuesday, eventually prevailed after two hours and 24-minute encounter against her Croatian opponent in blustery conditions. "So quite simple rule".
Kasatkina will next in the quarters meet No. 10 seed Angelique Kerber who rolled past No. 7 seed Caroline Garcia 6-1, 6-1.
Halep overcame a sluggish start to beat Wang Qiang 7-5-6-1 in the fourth round to book a last eight berth against Petra Martic in the California desert.
Williams has no official ranking after spending a year off the court, which means she can not be seeded for WTA events.
"I stayed so many weeks off with injury and now coming back, so I was a little bit exhausted". On the very next point, Martic hit a forehand wide as Halep took the game and a 5-3 set lead. He then walked to the net and ended the match.
In the men's draw, Philipp Kohlschreiber upset second seed Marin Cilic 6-4, 6-4 to advance to the fourth round on Tuesday.
Venus broke Sevastova winning the point of the match involving a drop shot after an exhausting battle from the baseline and a high backhand volley on the Latvian's lob and served out the 763rd WTA main draw win.
The 29-year-old Del Potro improved to 7-6 overall against Ferrer and his five consecutive victories date back to the 2013 Wimbledon quarter-finals.