Venus' defeat follows the shocking upset three days earlier of her sister, Serena, who suffered the most lopsided loss of her career: 6-1, 6-0 to Johanna Konta in the first round.
The Croatian number one was 3-0 up in the first set when the match resumed, and she wasted no time in racing to a 6-1 7-6 (7/0) victory.
Mertens, bidding for her fourth title of the year, moves into a semi-final against fifth seeded Romanian Mihaela Buzarnescu.
Williams has not advanced past the third round of a tournament since March and has yet to find the form that helped her reach two Grand Slam finals in 2017.
World No.49 Sakkari needed one hour and 43 minutes to dispatch Williams as she has rolled through her first three matches at this event without dropping a set.
Mertens broke Konta at love when she served for the opening set and saved two set points before forcing the tiebreaker.
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Konta backed that victory up with a 6-1, 6-4 win over Sofia Kenin.
"I'm so pleased and happy to be in the final, the third final of my career", Buzarnescu told reporters.
"Even after the first set, I thought she could come back, so it was really not easy". She closed out Collins by winning the final six points.
"If I will get top 20 - like my goal since I was 14 - that's going to be an awesome feeling".
At the Citi Open in Washington, number seven seed Donna Vekic will face former victor Svetlana Kuznetsova in the final. The two competitors had their match delayed by rain with Kuznetsova having won the opening set and the second set tied 2-2. China's Saisai Zheng had her match against American Allie Kiick postponed until Saturday.