The Williams sisters have won the title five times each out of the last 15 at the All England Club but it was Serena who triumphed in their first Grand Slam clash since the 2009 Wimbledon final.
Meanwhile, 2004 Wimbledon champion Sharapova, 2012 beaten finalist Agnieszka Radwanska and two-time Grand Slam winner Victoria Azarenka also booked their places in Tuesday's quarter finals.
All eight Wimbledon quarter-finalists from last year are out of the tournament, while Serena and Sharapova are the only two from the world's top 12 who are still standing.
US duo Madison Keys and Coco Vandeweghe, Switzerland's Timea Bacsinszky and Garbine Muguruza of Spain also made it to the last eight. Serena secured her 14th win in 26 clashes with Venus and the sisters hugged at the net after the match on Centre Court finished 6-4, 6-3.
Playing each other "definitely doesn't get easier", Serena said. "I was out there, I 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."
Serena to face Azarenka
As for the match, "it was really good for me to get it done in straight sets and just put this behind me and move forward", she said.
The 20-time Grand Slam champion remains on course to completing the feat of holding all four majors at the same time, having the US, Australian and French Open titles under her belt.
Serena faces Azarenka, the 2012 and 2013 Australian Open champion, in the quarter-finals after the Belarusian 23rd seed saw off the in-form Belinda Bencic, on a career-high ranking of 22, 6-2, 6-3.
Sharapova endured her toughest test so far but still made it through to the quarter-finals with a 6-4, 6-4 win over Kazakhstan's unseeded Zarina Diyas.
The Russian fourth seed won Wimbledon 11 years ago but has only made it past the fourth round once since 2006.
'Great position to be in'
"I thought I've been doing good but as we all know, it only gets tougher from here," the Siberian said. "It's a great position to be in. I lost at this stage last year so was extremely happy to go a round further."
She faces Vandeweghe in the quarter-finals after the US world number 47 edged out Czech sixth seed Lucie Safarova, last month's beaten French Open finalist, 7-6 (7/1), 7-6 (7/4). Vandeweghe had never been beyond the third round of a Grand Slam before this year's Wimbledon.
While Serena, Sharapova and Azarenka have 27 Grand Slam titles between them, there are no major winners at all in the bottom half of the draw, where 13th seed Radwanska is the highest-ranking player still standing after Caroline Wozniacki crashed out.
The Danish fifth seed, blew her chance to make the quarter-finals with a 6-4, 6-4 defeat to 20th seed Muguruza. Wozniacki, who has been the world number one despite never having won a Grand Slam, was the only top 12 player left in the bottom half of the draw.
Wozniacki in 4th round
Wozniacki has now reached the fourth round at the All England Club five times without ever progressing. Muguruza will face Bacsinszky for a place in the semi- finals.
The Swiss 15th seed, who reached her first Grand Slam semi-final at the French Open, recovered from a terrible start to beat world number 48 Monica Niculescu of Romania 1-6, 7-5, 6-2.
Polish 13th seed Radwanska booked her spot in the quarter -finals with a 7-5, 6-4 win over Serbian 28th seed Jelena Jankovic.
Former world number one Jankovic had knocked out defending champion Petra Kvitova in the third round. Radwanska faces 21st seed Keys in the quarter-finals.
The 20-year-old, an Australian Open semi-finalist earlier this year reached the last eight with a 3-6, 6-4, 6-1 win over Belarusian qualifier Olga Govortsova.