After a pair of scratchy wins in her first two rounds, Williams looked as sharp as ever this time against Vandeweghe, hitting 17 winners to just 11 unforced errors and fighting off all six break points she faced in the match. The No.1-seeded Williams would beat Vandeweghe, who was a qualifier, 63 61.
"It was a much tougher match than the scoreline showed," Williams said in her on-court interview afterwards. "CoCo has such an amazing serve, so every time I was returning I was like, 'Hopefully I can touch the ball.' But it was really good for me to win this match today. I love playing here in Miami."
Williams and Vandeweghe smiled and laughed at the net afterwards - what were they talking about?
"She said she wanted to play doubles with me," Vandeweghe said. "She said, 'Listen, you played so well. We've got to play doubles somewhere. I'm serious. We'd do so well. We've got to play doubles.'
"That was the kind of ins and outs of it. I don't know - I think I would have to get through Venus first to be able to play doubles with Serena, but whenever she wants to, I will play doubles with her!"
Williams was told in her press conference how excited Vandeweghe had been at the idea.
"Well, not as excited as I am, I don't think," Williams said. "I think we'd make a great team, actually. It would be really fun. I've been trying to just play around and see if I can ever play a tournament when Venus isn't there, and I just have some extra time on my hands and play some doubles matches."
The World No.1 was asked what impressed her so much about her countrywoman. "Besides the obvious? Well, she's improved a great deal. Her focus is so much better. Her movement is good. Her attitude is great. She's a nice girl. And it's always fun to play with young Americans and just enjoy it.
"It's just so good to see another American doing really well."
Williams has now reached the quarterfinals or better 13 times in 14 career appearances at the Sony Open Tennis. Her only pre-quarterfinal loss came all the way back in 2000, when she fell to Jennifer Capriati in the fourth round (Capriati would then fall to Sandrine Testud in the quarterfinals).
Next up for Williams will be the No.5-seeded Kerber, who recovered from a second set blowout to beat No.23 seed Ekaterina Makarova, 64 16 63. Makarova not only had a winning head-to-head record against Kerber going into the match, 4-3, but had also won their last two meetings in straight sets.
Williams leads Kerber in their head-to-head, 3-1. Kerber's win came at Cincinnati in 2012.