Wildcard Williams had not lost a set to the Belarusian in their three meetings prior to their second-round clash in Stanford, and despite a slip up late in the second set, the American posted a 6-4 7-6 (7-1) victory to move into the quarter-finals.
Azarenka, who played with a bandaged left thigh, saved two match points in the 12th game of the second set to force a tie-break.
But Williams ensured two-time major winner Azarenka remained set-less against her in their four matches - all of which have been on hard courts - racing to a 5-0 lead in the tie-break before advancing on her third match point.
Williams, ranked 25th, will take on Germany's Andrea Petkovic in the last eight at the WTA Premier tournament.
Serbian fifth seed Ana Ivanovic will play Venus' sister Serena in the quarter-finals, after dispatching of Canadian qualifier Carol Zhao 6-1 6-1 in 54 minutes.
Third seed Angelique Kerber of Germany overcame a second-set stumble to see off American Coco Vandeweghe 7-6 (7-4) 0-6 6-2 in two hours and eight minutes.
Kerber's next task will be Spain's Garbine Muguruza, who won a break-infiltrated contest over Slovakia's Daniela Hantuchova 6-4 6-4.
Of the 20 games the pair played, 10 were breaks of serve, with Muguruza advancing to her first quarter-final since reaching the French Open last eight.