The No.30-seeded Williams was the first of the pair to advance, rallying from an 0-3 first set deficit - and 4-1 down in the ensuing tie-break - to overpower Japanese No.1 Kurumi Nara, 7-6(4), 6-1.
Nara played very well - she compiled a +11 differential of winners to unforced errors (16 to 5). But Williams was completely on her game, putting together a devastating +30 differential (46 to 16).
"Walking out there you know no one's going to give you a match, especially at the majors, so I knew all points I would have to work for," Williams said. ""I think I was able to lift my game a little at the important points, which is what you want to do. Then also in the second set I lifted my game."
Despite losing, Nara was just as happy with the match - for a different reason. "It was very special for me because I saw Venus play when I was a child," she said. "I was very happy to play with her."
The No.6-seeded Kvitova followed with a 6-2, 6-0 victory over Mona Barthel, also putting together some very impressive numbers - a +16 differential (25 to 9). The Czech won 10 of her 11 net points.
"Venus is a big champion here as well," Kvitova said. "She likes the grass, and I'm totally the same. And I'm looking forward to this match. I think it's going to be a great fight. We played in Doha I think, and then in Tokyo, and it's always a very tough match, so I'm expecting the same thing here."
"I know I'll have to get out there and play better than her," Williams said of the match-up.
"That's really what it boils down to - the last point, make sure I'm winning it instead of losing it."
"You can always take something positive from the match, and I created a lot chances to make things happen, but I just didn't use any of those opportunities," Azarenka said. "It's consistency. It's not enough. It's a little bit too many mistakes and not closing the opportunities, not being sharp enough.
"There are a lot of things to be tuned and practiced - I basically need to get back to work."
Azarenka was the second Top 8 seed to go out here - No.7 seed Jelena Jankovic lost on Tuesday.
The other seeds all won, including No.2 seed Li Na, who cruised past Yvonne Meusburger, 6-2, 6-2, and No.4 seed Agnieszka Radwanska, who outdid Casey Dellacqua, 6-4, 6-0. No.10 seed Dominika Cibulkova, No.16 seed Caroline Wozniacki, No.22 seed Ekaterina Makarova and No.23 seed Lucie Safarova were also among the winners as the bottom half of the draw played second round.