Three-time winner Williams lost serve three times in the opening set as the first six games went against serve before the American got on track, breaking the 17th-seeded Russian in the 12th game to end the opening set.
Williams, who has yet to lose a set, got on a roll after that, losing just three points on serve in the second set and ending the 79-minute match with her sixth ace.
“I had a few errors in the beginning,” Williams told the Arthur Ashe Stadium crowd after the quarter-final. “But I’m happy that I’m through and I’m really excited.”
The 29-year-old American, playing just her sixth tournament this year after being sidelined by injuries and health concerns, will play either top-seeded Caroline Wozniacki of Denmark or 10th seed Andrea Petkovic of Germany in the last four.