Sania did not let the two previous defeats at the hands of Golovin affect her game as she demolished her rival, completely dominating the proceedings with her powerful forehand.
The 20-year-old Hyderabadi lass served efficiently, ate up the Frenchwoman's second serves and won the match with a blistering forehand winner crosscourt.
''She said to me, 'can you hit it any harder?''' the world number 35 added with a laugh.
''She's one of my closest friends on tour and it's never easy to play a friend,'' she added.
She said Golovin's ability to retrieve well led her to adopt an aggressive game from the start.
Sania is playing in her third consecutive Bank of the West Classic and will be making a quarterfinal debut at the tournament.
Quickly becoming a fan favorite and drawing the largest crowds of the tournament, Mirza has been thrilling spectators throughout the week highlighted by a classic three-set battle with Akiko Morigami Tuesday night in front of 3,000 fans.
The victory set up a quarter-final showdown with fourth seed Patty Schnyder of Switzerland, who registered a 7-5 6-2 win against Russian Yaroslava Shvedova.
Meanwhile, top seed Anna Chakvetadze looked good for another career title after her n victory Cincinnati Open victory as she continued her good run of form with a comprehensive 6-4 6-1 triumph against Greece's Eleni Daniilidou.
Sania had gone down to Chakvetadze in the semifinals of the Cincinnati Open last week.
In another upset match, Belarusian qualifier Olga Govortsova belied her lowly ranking with a 4-6 7-5 6-2 victory over Sania's doubles partner, the fifth seeded Israeli Shahar Peer to move into the quarter-finals of the Stanford Classic.
In the doubles draw, the third seed controversial Indo-Israeli duo of Sania and Peer dug deep to register their doubles quarter-final berth, beating off the challenge posed by 11th seeds Tatiana Poutchek of Belarus and Anastasia Rodionoa of Russia.
The Indo-Israeli will now face unseeded pair of Akgul Amanmuradova of Uzbekistan and Angelika Bachmann of Germany in the 600,000 dollar Tier II tournament.
Sania, partnering Bethanie Mettack of the US, claimed her second doubles title of the year at Cincinnati last week.