The world number two was an emphatic 6-2, 6-2 victor to leave five-time Grand Slam champion Sharapova still searching for her first title since returning from a doping ban in April.
Halep took a tough loss to the Volvo Car Open champion just last week at the Dongfeng Motor Wuhan Open - her first in three meetings - but played with clear intent of restoring order to their head-to-head on the National Tennis Stadium, striking 19 winners to 21 unforced errors to dismiss the unseeded 20-year-old in little over an hour. Now there is a possibility of a fifth World No 1 just this season (including Serena) with Simona Halep and Elina Svitolina going for glory in Beijing at the China Open.
Kvitova, who produced 33 winners offset by 43 unforced errors, said she was exhausted but very happy with the victory, and will meet Caroline Garcia in the last four. On the court I felt pretty slow. Her win advanced her to the quarterfinals. "I'm already happy. I love these big matches anyway, so I will do my best tomorrow".
Respect: Maria Sharapova and Simona Halep meet at the net after their third-round battle at the 2017 China Open. "She did all the right things".
French Open champion Jelena Ostapenko beat Sam Stosur 6-3 7-5 in the second round and qualified for her maiden appearance at the WTA Finals later this month.
Halep goes through to the quarter-finals where she will face Kasatkina, who started slowly but grew in confidence to see off Radwanska 4-6 7-5 6-2.
She could yet be joined by Wuhan Open champion Caroline Garcia, who boosted her chances with a 7-6 (7/4) 6-4 victory over Elise Mertens.