The American is the fourth seed at this event and with the top three players all withdrawing, was a huge fan favourite against the ninth-seeded Russian.
"I've never played in front of a crowd that's really, really been so behind me," Williams said.
The partisan support had a lot to be happy about as did Williams, who won four straight games in the second set to close out the match.
In other quarter-final action, 11th seed Patty Schnyder caused the biggest upset of the round when the Swiss left-hander defeated fifth-seeded American Lindsay Davenport 6-3, 6-2.
Schnyder needed just 52 minutes to end Davenport's good run of form that stretched back to the Californian's win at Amelia Island last week.
Davenport lost the first four games of the first set and never seemed to recover.
In the semi-finals, Williams plays Croatia's Jelena Kostanic, who defeated Hungary's Petra Mandula 7-6, 6-2 to stay on course for her first tour victory.
Schnyder meets 16th-seeded Conchita Martinez of Spain in Saturday's other semi-final.
Martinez celebrated her 32nd birthday in style, easing past eighth-seeded Nadia Petrova of Russia 6-3, 6-1.
