The turning point came after a string of unforced errors left Halep trailing 5-4 in the first set, prompting coach Darren Cahill to tell the defensive specialist to work longer points and reduce the error count. "I did exactly what he said after that".
She was the last Chinese singles player standing in the California desert.
"I'm just going on court and actually now enjoying every minute during I'm playing", 20th seed Kasatkina told reporters.
"She has everything in her game", Venus said of Sevastova. She has everything in her game.
Venus Williams survived a hard fourth round test to beat Latvia's Sevastova 7-6, 6-4 just one day after beating sister Serena in a third round contest.
Halep took time out to head to the stands and watch the Williams sisters face off for the 29th time in their career in the ongoing Indian Wells WTA tournament.
Halep is the only former Indian Wells victor left in the women's draw after World No.20 Daria Kasatkina upset World No.2 Caroline Wozniacki 6-4, 7-5.
Tuesday's quick victory came two days after Halep needed over two hours to eliminate American teenager Caroline Dolehide 1-6, 7-6 (7/3), 6-2.
"I wasn't missing that much", the 26-year-old Romanian player said after the match. "I dominated a little bit more".
"I missed too many shots in the first set".
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.
Williams, who is the oldest female player in the draw at 37, rallied back in the second set to book her spot in the quarter-finals.
Pliskova, using her powerful serve, overwhelmed 16-year-old Amanda Anisimova to advance to the last eight for the third year in a row.
Halep overcame a rough start against China's Qiang Wang to advance 7-5, 6-1, while Williams kept her momentum moving forward with a 7-6 (6), 6-4 victory over No. 21 seed Anastasija Sevastova.