The top-ranked Williams seeks a record seventh Key Biscayne title.
Williams, who owns a small share of the Miami Dolphins, wore a dress in the team's orange and turquoise colors. As with the Dolphins, she found points tough to come by in the early going.
She erased a 5-3 deficit in the first set, then fell behind 6-3 in the tiebreaker. Shvedova pushed a forehand into the net, then the Kazakh hit a nervous double-fault that allowed Williams to exhale.
She won the next two points with aces, then closed out the set with a backhand winner, a fist pump and a scream of "Yes!"
Lleyton Hewitt became the third active man to win 600 matches when he rallied past Robin Haase of the Netherlands 3-6, 6-3, 6-3 in the first round.
Hewitt joined Roger Federer (942 wins) and Rafael Nadal (675) in reaching the milestone.
"Not many people get the opportunity to get close to that, so it means I have been around for an awfully long time," the 33-year-old Hewitt said. "I'm getting old. A few years ago when I had the last couple of surgeries, I probably would have doubted I'd get to this stage. I'm grateful I'm out there and able to compete with the best guys."
Hewitt is a former No. 1 and a three-time Key Biscayne semifinalist.
Fellow Australian Bernard Tomic, mounting a comeback from surgery on both hips and playing for the first time since January, lost to Jarkko Nieminen of Finland 6-0, 6-1.
In women's play, No. 5-seeded Angelique Kerber of Germany won her opening match, beating Peng Shuai of China 6-3, 1-6, 7-6 (5). Kerber, a two-time Grand Slam semifinalist, matched her best showing at Key Biscayne by reaching the third round.
Ana Ivanovic beat American Lauren Davis 6-1, 6-1, and No. 8 Petra Kvitova defeated Paula Ormaechea of Argentina 6-3, 6-4. Svetlana Kuznetsova, the 2006 champion, lost to Croatian qualifier Donna Vekic 7-6 (5), 7-5.
Maria Sharapova was scheduled to play her opening match late Thursday. Seeded men begin play on Friday.
