"I think I returned well", she said. "I just couldn't execute as well as I wanted to".
Despite being at the top of the rankings, Halep is yet to win a Grand Slam, having recently lost to Caroline Wozniacki in the final of the 2018 Australian Open in January.
The American won a remarkable 23rd Grand Slam at the 2017 Australian Open previous year when she defeated her sibling Venus in the final in a 6-4, 6-4 win. "He hits it big, has a big serve, big forehand", said Federer, a five-time champion at Indian Wells.
Wozniacki had a chance to take it back but she needed to win the Indian Wells title to do it.
Simona Halep and Angelique Kerber cruised into the Indian Wells Masters quarter-finals, but Caroline Wozniacki departed.
Federer will next face South Korea's Chung Hyeon, who defeated Uruguay's Pablo Cuevas 6-1, 6-3.
Halep called for a time-out in the first set so her coach, Darren Cahill, could come to the court to discuss strategy.
"So I'm just somebody who is also playing tennis".
"I knew that I had to really pay a lot of attention when I was serving, because it could have turned into one of those matches where holding serve is very important". "So it was a good chat".
"I was honestly quite surprised how quickly he came back", Federer said.
"I'm just going on court and actually now enjoying every minute during I'm playing", 20th seed Kasatkina told reporters.
In her second career semifinal, Osaka will seek her first win over Simona Halep at the fourth attempt.
The fifth-seeded Pliskova battled past American teenager Amanda Anisimova 6-1 7-6 (7-2), ending the 16-year-old's fine run. "It was tough to play, because the ball was really moving, but I just tried everything". Pliskova, supposed to rely on serve and forehands, continued to lose nearly every point when Osaka attacked her off the stronger side.
Williams, a 23-time Grand Slam champion and the most successful player of the Open era, was knocked out by her sister Venus in round three in California. She looked relaxed and extremely confident while Pliskova struggled to hit the spot with her serve, despite her 20 aces in the first three matches, the most of the players left, and to be effective in return.
Venus next faces Carla Suarez Navarro, who rolled past Danielle Collins 6-2 6-4.