Kuznetsova won Grand Slam titles at Flushing Meadows in 2004 and the French Open last year, and also was the U.S. Open runner-up in 2007.
She had lost her most recent two matches against Kirilenko, both on clay this season, but was in control pretty much throughout Saturday. Kuznetsova saved both break points she faced and finished with a 30-12 advantage in winners.
Next for Kuznetsova is a match against 45th-ranked Dominika Cibulkova.
Kirilenko fell to 0-5 in third-round matches at Flushing Meadows. She was the junior girls' champion at the 2002 U.S. Open.