It's a huge win for the No. 63 Williams, who defeated No. 34 Mona Barthel in the first round. Williams is unseeded at this tournament.
It's another sign that the former No. 1 may be getting back to form. Williams also upset then No. 15 Kirsten Flipkens in the first round of the U.S. Open.
Azarenka, who lost to Serena Williams in the U.S. Open final two years in a row, hasn't faired well against the First Family of tennis.
Winner of seven Grand Slams, Venus Williams has struggled since she announced she has Sjogren's Syndrome. The autoimmune disease causes marked fatigue.
Another problem for Williams is the lack of match play. She entered this tournament with only 20 matches under her belt this year. Her sporadic play caused her drop from the Top 50. It also meant having to face tougher opponents in early rounds.
Facing Azarenka, it appeared Williams might suffer another early-round elimination.
But she took control early, taking the first set 6-2. Azarenka mounted a comeback. Down a break in the second set, she broke back to level the match at 4-4. However, in her bid to go up 5-4, Azarenka was broken again.
Azarenka was serving at 30-40 and hit what she believed was an ace. But the ball was called out. She challenged the call and the review showed the ball was in. The chair umpire ruled that Azarenka got another first serve. But Azarenka thought Williams didn't have a play on the ball and argued that it should have been an ace.
An angry Azarenka served again. After a short rally, she hit the ball out, giving Williams the break. Williams sealed the match with her best service game.
Williams faces No. 13 seed Simona Halep in the next round.