Wozniacki, who has won a WTA-leading five titles this year, led 5-1 in the second set. However, the No. 22-ranked Italian stormed back with three break points to complete the upset.
"This is the best victory in my life," the 28-year-old Vinci said.
Williams, a 13-time Grand Slam tournament champion, used her potent serve, which topped out at nearly 122 mph, to roll through her first set before the 20th-ranked German improved in the second.
"I thought (Goerges) played really well and really smart, the conditions were extremely tough," said Williams of wind gusts up to 22 mph. "She had to change up her game and I had to adjust to that."
Wozniacki had a bye in the first round and never really got going against the 22nd-ranked Italian, sending her return long on match point. Wozniacki also hit returns long twice at the first set point.
"I would have liked to have won that one and especially after leading 5-1 in the second," Wozniacki said. "It's not fun to lose this, but there's nothing really I can do about it now, just practice, and try to do better."
Windy conditions wreaked havoc with Wozniaki's serve in the first set, as the ball repeatedly floated away when she tossed it above her. She had seven double-faults in the match.
"It was very difficult at first with the wind," Wozniacki said. "Especially when you threw it up. It was going everywhere, so definitely that didn't make it easy. It was blowing in different directions, but it's the same for both players."
Vinci reached the third round of the Rogers Cup in her third time in the tournament. She has wins this year in Barcelona, Budapest and Hertongenbosch.
"I was 5-1 down but I knew that I can win the set because it was a lot of wind, so some mistakes," she said. "I tried to stay focused and play aggressive. That's it, this is the key why I won the set."
Williams laughed when asked if her powerful serve gives her an advantage in the wind.
"I had to hit it softer today because it was so windy, I had to take pace off my ball," she said. "If you hit it too hard the ball is going to totally fly the harder you hit."
Sharapova's serve abandoned her in a second set, when she committed five double-faults. The three-time Grand Slam champion won when Jovanovski hit a return long.
"I expected my opponent to play well today because she's dangerous, although she's a qualifier she's someone who's moving up and young and eager, and has beaten good players before," Sharapova said. "She's on her way up. So I knew that it was going to be a dangerous round knowing she had played a few matches already and this was my first match."
Also, Ana Ivanovic defeated Iveta Benesova of the Czech Republic in a match moved from center court after the wind blew a light onto the surface. Francesca Schiavone of Italy eased into the third round with a 6-1, 6-3 victory over Ekaterina Makarova of Russia.
Samantha Stosur downed Canada's Aleksandra Wozkiak 6-3, 6-4.
"Well, it's disappointing," Wozniak said. "You play at home and you want to do so well. But I thought it was a good match, and I had a really tough opponent."
"It is sad for her," Li said. "Always tough when you're playing same-country player. We train together."