The second seeded American, eyeing her seventh title here, smashed 15 aces and 35 winners in the 86-minute clash against the Czech Republican.
The match featured a combined 59 winners and 23 aces to just 39 errors.
"The last time we played was in the final of a Grand Slam ... it wasn't easy. I'm really happy to have gotten through that," Williams was quoted as saying by the tournament's website after the match.
"Definitely played two really tough opponents (in the first round she beat former top-10 player Belinda Bencic), but it's a great way to start the tournament."
Next up for the American is compatriot Nicole Gibbs in round three.
Earlier, third seed Agnieszka Radwanska was stunned in the second round 3-6, 2-6 by Croatia's Mirjana Lucic-Baroni.