The No.16-seeded Williams put together a very impressive +16 differential of winners to unforced errors on the day, 29 to 13. That 29 winners in 42 minutes is about a winner every minute and a half.
"She's had a great last 52 weeks. She's had really great results in the majors. Playing a higher-ranked player in the first round is a challenge, but everything worked out for me," Williams said.
"I don't think she played badly. I was just able to convert on the important points."
Earlier in the day, sister Serena Williams also advanced to the second round, recovering from a 3-1 hole in the first set to beat inspired Russian qualifier Margarita Gasparyan in straight sets, 6-4, 6-1.
When the draw came out, everyone was talking about the top section, which includes both Williams sisters, both five-time Wimbledon champions - they could play each other in the fourth round this year.
"Well, she's been really tough, and the last time we played, she actually beat me," Serena said.
"That's not going to be an easy match, but I'm just going to focus on right now first."
The other Top 8 seeds in action all advanced, with No.4 seed Maria Sharapova beating British wildcard Johanna Konta, 6-2, 6-2, No.6 seed Lucie Safarova rallying from 6-3, 5-3 down to beat Alison Riske, 3-6, 7-5, 6-3, and No.7 seed Ana Ivanovic cruising past Chinese qualifier Xu Yi-Fan, 6-1, 6-1.
Carla Suárez Navarro, the No.9 seed, wasn't so lucky, falling to Latvian wildcard Jelena Ostapenko, the junior Wimbledon champion a year ago, 6-2, 6-0. It was the first Top 10 win of Ostapenko's career.
Other winners included No.11 seed Karolina Pliskova, who beat Irina Falconi for her WTA-leading 36th match win of the year, 6-4, 6-1, No.14 seed Andrea Petkovic, who defeated Shelby Rogers, 6-0, 6-0, and No.23 seed Victoria Azarenka, who brushed aside Estonian wildcard Anett Kontaveit, 6-2, 6-1.
? EleVen by Venus (@EleVenbyVenus) June 29, 2015