In the 26th career meeting between the siblings, Serena dominated with her steady serve and big hitting from the back of the court to win 6-4, 6-3 on Centre Court in 1 hour, 8 minutes, extending her Grand Slam winning streak to 25 matches.
The win sent the top-ranked Serena into the Wimbledon quarterfinals as she bids for a fourth straight Grand Slam title, a feat last accomplished by the younger Williams in 2003.
With Madison Keys and Coco Vandeweghe also winning Monday, it's the first time that three American women have reached the Wimbledon quarterfinals since Serena, Lindsay Davenport and Jennifer Capriati did it in 2004.
If Serena can triumph again, only the U.S. Open would stand in her way of becoming the first player to complete a calendar-year Grand Slam -- a sweep of all four majors in the same season -- since Steffi Graf did it in 1988.
"I don't think she's done, so we'll see what more she does," Venus said when asked if her sister might be the greatest women's player of all time. "I don't think she would call herself the greatest player of all time, because she respects everyone else and the accomplishments they've made.
"But the level she's playing at is unprecedented. I can say that with confidence. So make what you will of it. Then, when it's a wrap, it will be easier to make labels and not offend anybody."
When Venus hit a backhand long on break point to end the match, Serena showed no emotion and did not celebrate. She walked slowly to the net, where the two sisters hugged. They walked off the court together.
"It's hard to feel excited about [beating] someone you root for all the time no matter what and who you love so much and she's your best friend in the world," Serena said. "It's never easy, but you just play for the competition and enjoy the moment."
Both sisters have won Wimbledon five times, but Serena also has a total of 20 Grand Slam titles. Another Wimbledon title will put her just one behind Graf, who holds the Open era record with 22.
"It was really good for me to get it done in straight sets and just put this behind me and just move forward," Serena said.
Monday's victory improved her career record against Venus to 15-11, including 8-5 in Grand Slams and 4-2 at Wimbledon. This was the sisters' first meeting at a major since the 2009 Wimbledon final, which was won by Serena.
Serena broke twice in each set and lost serve just once. She had 10 aces, as well as a total of 26 winners and 13 unforced errors.
"I think I served well today," she said. "I didn't hit huge serves, I hit one big serve, but other than that I think I just was really consistent with my serve. She was playing really well, so at the end I was able to come through."
Venus Williams was playing in her 18th Wimbledon. She was the oldest remaining woman in the draw at 35.
"It definitely doesn't get easier," Serena said. "But today I was out there and I just thought, `Wow, I'm 33, and she just turned 35 -- I don't know how many more moments like this we'll have.'
"I plan on playing for years, but you never know if we'll have the opportunity to face each other. I just took the moment in and I thought, `We're at Wimbledon.' I remember when I was 8 years old, we dreamed of this moment, and it was kind of surreal for a minute there."
Vandeweghe upsetting French Open runner-up Lucie Safarova of the Czech Republic in straight sets, dominating both tiebreakers to win 7-6 (1), 7-6 (4) after the players traded breaks once in each set.
Vandeweghe advanced despite what she called "one of my worst matches that I played the whole tournament so far," and she said she knows she needs to play a lot better against Sharapova.
"I try to have a good time out there on the court, or at least fake it enough to where it looks like I'm having a good time out there," Vandeweghe said. "I definitely am the type of person that likes to have a laugh at themselves, especially when it looks like I have done something stupidly ridiculous. I think that relaxes me instead of keeping it pent up and at a shorter fuse."
The 21st-seeded Keys reached the Wimbledon quarterfinals for the first time, beating Olga Govortsova of Belarus 3-6, 6-4, 6-1.
"It's been a while since there has been that many Americans in the second week, and it's just really exciting," said the 20-year-old Keys, who reached the Australian Open semifinals this year. "I think it's going to kind of inspire everyone else to keep doing well and keep working hard. ... It's great that Coco went out and won today as well."
Muguruza, the 20th-seeded Spaniard who reached the quarterfinals at the French Open the last two years, beat No. 5 Caroline Wozniacki of Denmark 6-4, 6-4; Bacsinszky rallied to beat Monica Niculescu of Romania 1-6, 7-5, 6-2.
The Associated Press contributed to this report.