Williams looked in no mood to follow men's top seed Novak Djokovic out of tournament after his shock defeat on Saturday and treated the middle Sunday party crowd to an imperious 51-minute performance.
Warning her last-16 opponent, Russian Svetlana Kuznetsova, that there is more to come, she said: "I thought it was good, I still want to get out to a little bit of a faster start but I was really focused and calm today."
Williams was broken by unseeded Beck in her second service game but then stepped it up and never looked back.
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She thundered down the biggest women's serve of the grasscourt major so far at 123 mph (198 kph), followed by an ace, to seal the first set against the 22-year-old.
The 34-year-old American, who said she had been helped by suffering a scare in round two against compatriot Christina McHale, romped through the second set in 20 minutes as Beck's resistance crumbled.
The match brought her 300th grand slam win - something that seemed to take her by surprise.
"No? Was it? Cool, oh nice. I had no idea, that's awesome, right? I think that is a lot of matches," she said as she came off court.
DIZZYING ARRAY
The statistic, just one of dizzying array for the six times Wimbledon champion, takes her past Chris Evert on 299 and leaves her behind Martina Navratilova on 306 after what, by Williams's standards, has been a disappointing spell.
She lost the French Open final to Spain's Garbine Muguruza, and was beaten in the Australian final by Angelique Kerber.
She also lost in the U.S. Open semi-finals last year, robbing her of the chance to hold all four major titles in the same season after netting four in a row with last year's Wimbledon win.
With those losses, perhaps the most glittering number of them all still eludes her.
Williams is continuing her quest for at least one more slam to equal or better Steffi Graf's Open era record of 22 major titles, although she believes she has already etched her name in the history books, alongside Djokovic.
"I think he and I have both made extreme history. He's won four in a row. I won four in a row last year. I think that's historic in itself," she told reporters.
Her next opponent, old foe Kuznetsova, reached the Wimbledon fourth round for the first time in eight years with a 6-7(1) 6-2 8-6 win over American Sloane Stephens.
"I'm looking forward to it. We both are ready for this match. You know, we're both going to give it our heart, as we always do when we play each other," Williams said.
"I know what it takes to win these tournaments. It's just about now just doing it."
(Editing by Ed Osmond)
