The result means only two players -- Jelena Jankovic of Serbia and Vera Zvonareva of Russia -- remain in contention for the last spot for next week's season-ending WTA Championships in Doha.
Jankovic is five points ahead of Zvonareva in the battle for a berth. Both players advanced Tuesday to the second round.
Kirilenko, ranked 61st, opened with a break and saved four break points in the eighth game. The 10th-ranked Radwanska then dropped serve again to lose the first set, and called for a trainer afterward to treat her right thigh.
Kirilenko broke decisively in the second game of the second set. She saved a break point in the seventh game before securing her first win in five appearances at her hometown tournament.
Earlier, qualifier Evgeniya Rodina beat sixth-seeded Elena Vesnina 6-1, 3-6, 6-2 in an all-Russian match.
On the men's side, fifth-seeded Pablo Cuevas of Uruguay advanced to the quarterfinals, rallying to beat Teimuraz Gabashvili of Russia 3-6, 6-1, 6-4.
Seventh-ranked Nikolay Davydenko, who won the Shanghai Masters on Sunday, was scheduled to later face Marat Safin in a first-round match.
The 20th edition of the dual ATP and WTA Kremlin Cup has a weakened women's draw because seven of the world's top players have already qualified for the Doha Championships and have opted to skip the Moscow tournament.