Belarusian Azarenka, making her first appearance of the week, cruised to a 6-3, 7-5 win against Michaella Krajicek of the Netherlands before American wildcard Williams upset third seed Kvitova 6-4, 4-6, 6-0 in an evening match.
Azarenka is off to the hottest start to a WTA season since Martina Hingis won her first 37 matches in 1997. The Belarusian's wins this year include the Australian Open and Indian Wells last week, but she realizes she now has a target on her back.
"I felt that she had nothing to lose, so she went for her shots, she was really aggressive," Azarenka told reporters.
"I think I could have been more aggressive and play more my game, but I found the right shot selection and the right opportunities when I needed." Former world number one Williams, playing in her first WTA event since last year's US Open, broke Czech Kvitova three times in the final set.
"The third set was very cruel for me," left-hander Kvitova said. "The first two games I had game points and break points, but I didn't make it.
"Then it was tough to still focus on my plan for the rest of the match. I knew what I had to do today but, if I wasn't returning very well, it's tough to play against her.
"She looks very ready, very fit. She's back," the Czech said of Williams, who revealed at the US Open she had been diagnosed with Sjogren's syndrome, an auto-immune disease that causes fatigue and joint soreness.
In the ATP event in Miami, British fourth seed Andy Murray and second-seeded Spaniard Rafa Nadal breezed into the third round.
Murray, who was given a bye in the first round, rebounded from his early exit at Indian Wells last week to beat Colombia's Alejandro Falla 6-2, 6-3.
"I was expecting it to be tricky ... and managed to play better," said Murray, who will next face big-serving Canadian Milos Raonic, a 7-6, 6-2 winner against French qualifier Arnaud Clement.
"Once I settled down and started playing well, I was in most of his service games. So I was putting pressure on him." Left-hander Nadal made short work of Santiago Giraldo, hammering the Colombian 6-2, 6-0 in just over an hour.
American John Isner maintained his great run of form, which has included a win over world number one Novak Djokovic at Indian Wells, by defeating Russian Nikolay Davydenko 2-6, 6-3, 6-4, highlighted by 10 aces.
