Radwanska will next face Elina Svitolina of Ukraine, who followed up her surprise win over world number one Angelique Kerber by easing past Australia's Daria Gavrilova 7-6(3) 6-1.
Due to Thursday's rain in Beijing, Shvedova was forced to play twice, earlier beating Alize Cornet 6-2 6-4.
Fatigue appeared to catch up with Shvedova as Radwanska lost just three games to seal her third China Open semi-final in the last four years.
Battling Konta beaten by Radwanska in final
The eighth-seeded Keys led by a set and a break and appeared to be in control of her quarter-final clash against Kvitova, but the Czech, winner of last week's Wuhan Open title, fought back to level the match in a tiebreak.
The 21-year-old Keys raced to a 3-0 lead in the deciding set, but was once again pegged back by the 14th-seed. Keys eventually held her nerve to triumph in a tiebreak after 2 hours and 41 minutes on court.
Keys, who edged closer to qualifying for the WTA season-ending finals in Singapore, will next face Britain's Johanna Konta.
Konta lost the first four games against home-favourite Zhang Shuai, but then reeled off 12 in a row to win 6-4 6-0.
"Jo is playing really well," Keys told the WTA website (www.wtatennis.com).
"I mean, at this point everyone's trying to qualify, everyone's trying to play their good tennis at the end of the year.
"Pretty much whoever you play is going to be a tough match."
Konta through to third round in Beijing
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