Williams, a three-time champion at the Premier Mandatory-level event in 1998, 1999 and 2001, looked sharp on serve - she won 69% of her first serve points and 54% on her second serve - and broke Schmiedlova five times in the match to move through in exactly an hour and a half, 63 63.
"I felt good," Williams said. "She's competitive, a new player, and you never know what their game is really going to be like. I had never seen her play. But it's obviously great to be in the next round."
Williams is playing for the first time since Dubai, where she won the Premier-level Dubai Duty Free Tennis Championships and reannounced herself as a major threat in the game - it wasn't just her first WTA title since 2012, it was her first Premier-level title since winning the same tournament in 2010.
"I've been working hard on my game," Williams said. "I had some tough losses where I just wasn't able to kind of turn around. But they were always really close, and I kept putting myself in good positions to win matches. So I just started crossing over the line in Dubai - even the week before, I basically won the match but lost it somehow. I learned a lot from that one, too, and just kind of kept coming up.
"And I've been working hard since Dubai. I feel really confident in every situation on the court."
Williams was also asked how it felt to come into such a big tournament on a winning streak again.
"I feel like I've had a chance to play more matches this year than many, many years, like four or five. So I think that's been a great advantage for me, as well. I'm looking forward to playing this tournament obviously, and the Family Circle, as well. I'm looking forward to playing my third round match here.
"My whole plan is to be playing, and that's it."