The 105th-ranked Korolev double-faulted twice at 30-30 to lose his serve in the first game of the second set and trailed 0-2. But the Russian rallied to win six of the next seven games.
In the third set, Korolev squandered a 3-1 lead against the 91st-ranked Kendrick and trailed 5-4. But Korolev, cheered on by his cousin Anna Kournikova in the stands, won the next three games to clinch the match.
Korolev will play Guillermo Garcia-Lopez , who rallied to defeat Gilles Muller of Luxembourg 5-7, 6-3, 6-3.
"It's my second quarterfinals of the year because I played quarterfinals in Johannesburg,'' Garcia-Lopez said. "So it's good chance to keep playing better for the year.''
After splitting the first two sets, Garcia-Lopez took a 3-0 lead in the third set. But Muller tied it 3-3 before Garcia-Lopez closed out the match.
Later Wednesday, second-seeded Sam Querrey of the United States plays Christophe Rochus, and eighth-seeded Lu Yen-Hsun faces Stefan Koubek.
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