Although the Chinese eventually stopped the rot with a break of her own, Halep soon took charge again and cruised to an ultimately routine victory.
The 20-year-old Kasatkina improved to 11-6 on the WTA Tour season as she seeks to better her quarter-final appearance here in 2016.
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.
Earlier, Halep breezed through her fourth round match on with a 7-5, 6-1 victory over China's Wang Qiang.
Halep advances to the quarter-finals where she will face unseeded Petra Martic of Croatia who beat Czech Marketa Vondrousova 6-3, 7-6 (7/4).
Halep needs to reach the final at the Tennis Garden to retain her place at the top of the WTA rankings from Dane Caroline Wozniacki.
"I think she should have been actually number one seed in this tournament because she left as number one in the world".
Former S.Korean president Lee to be questioned
Lee has been lashing out at what he calls political retribution against conservatives by the government of President Moon Jae-in. Before he entered the prosecutors' office, Lee announced to reporters that he is in a "position of bad discomfort today".
Juan Martin del Potro beat Spaniard David Ferrer 6-4 7-6 (6-3) and will play fellow Argentine Leonardo Mayer, who defeated Japan's Taro Daniel 6-4 6-1.
Venus next faces Carla Suarez Navarro of Spain who rolled past Danielle Collins 6-2, 6-4.
"I'm playing my best matches against the best players", she said. Halep reclaimed the ranking just before Indian Wells.
Halep, bidding to become the 12th top seed to lift up the trophy and repeat her 2015 title-run, will spend her 18th and 19th weeks as World No.1 during Indian Wells, moving her past Jennifer Capriati (17 weeks) and Jelena Jankovic (18 weeks).
Halep called for a timeout in the first set so her coach Darren Cahill could come down to the court to discuss strategy.
"She has everything in her game".
Former world number one Karolina Pliskova also made it through to the quarter-finals, beating 16-year-old Amanda Anisimova 6-1 7-6 (6-2). She is on the verge of her second career singles title at Indian Wells. I just want to have the plan what I have to do.
Tyne Daly and Sharon Gless played the title characters in the original Cagney & Lacey, which ran on CBS for seven seasons. Another reboot is coming to TV, and this time it's the 80s iconic show Cagney & Lacey that will be brought back to life.
Moreover, the manufacturing which has a weight of 77.63 per cent in the IIP is showing the sustenance of the growth momentum. For core CPI, we expect some reversal of the strength in January and forecast an increase of 0.1% m/m and 1.7% y/y.
Here's some good news you probably weren't expecting today: the beloved V-Rally series is returning after a long 15-year hiatus. The V-Rally franchise hasn't been seen in 15 years and it's being brought by back with help from a developer from V-Rally 3.
Gorakhpur bypoll is a battle of prestige for the BJP as the parliamentary seat had been represented by Yogi Adityanath five times. The counting will be done for 14 constituencies in which there will be 26 rounds.
So if there are those issues with China, let's deal with those, not necessarily make it for everyone to pay these higher costs". He said the difference is "trivial ". "We are looking to make sure that USA companies can compete fairly around the world".
That could explain the small stroke that the man was found to have suffered and caused his left-side weakness. The MRI also revealed that the patient had experienced a small stroke related to the air pocket in his brain.
Anyway, the Broncos have their starting quarterback. "Obviously we've got to get better at that position". There were some things we should have done, that we should have done differently that we didn't do.
Press secretary Sarah Sanders defended the jibe and denied any rift, insisting Trump "made a joke, nothing more than that". It was long rumored that this was in the works because of continual disagreements between Tillerson and the White House.
Patten Group Inc decreased Southwest Georgia Financial Corp (NYSEMKT:SGB) stake by 977 shares to 50 valued at $21,000 in 2017Q3. Telsey Advisory Group has "Outperform" rating and $34 target. (NYSE:T) earned "Buy" rating by Citigroup on Friday, November 10.
The aviation sector in the country may remain affected with IndiGo and GoAir likely to face more disruptions in the coming weeks. In an announcement on its website during the day, IndiGo said it has cancelled 47 flights across its domestic network for today.
Qualcomm slays a lion, baits a dragon
A takeover of Qualcomm by Broadcom would have created the world's third-largest maker of microchips, behind Intel and Samsung. Only five takeovers of American firms have been blocked by US presidents on national security grounds since 1990.
White House says Trump still wants gun change
Sarah Sanders, the White House press secretary, has said the President wants to expedite the court process, not circumvent it. "To no one's surprise, the president's words of support for stronger gun safety laws proved to be hollow", said Sen.
De Boer is worst manager in history-Mourinho
De Boer, though, suggested after the game that Rashford would be better off playing under a manager other than Mourinho. If he was coached by Frank, he would learn how to lose because he lost every game.
Country star Tim McGraw collapses onstage during Ireland show
Faith walked alongside him in a dark turtleneck and jeans with long winter coat and covered her blonde locks with a baseball cap. The country music superstars were the headliners on the opening night of Country To Country music festival at London's O2 arena.
Apple Buys The 'Netflix For Magazines'
Texture acquisition comes as Apple tries to ramp up its services business which already includes Apple Music and the App Store. In other words, Cue said Apple is focused on the next big thing, rather than the thing that is big now.