The Greek fifth seed took just 68 minutes to eclipse her second-seed opponent 6-2 6-3 in a near-flawless performance.
In her on-court interview after the win, Sakkari said: "I think I just have to keep doing what I've been doing.
"I'm trusting myself. I'm just fearless on the court. I'm enjoying myself here.
"There's no secret behind how I'm playing, it was about time to start playing good again. I'm just very happy that it's actually happening here."
The victory ensures Sakkari will avoid world number one Iga Swiatek in the semi-finals, and will instead face either Caroline Garcia or Daria Kasatkina.
Swiatek will meet Aryna Sabalenka in the final four, after the seventh seed kept her tournament alive with a 6-3 7-5 win against Jessica Pegula.
Pegula is now 0-6 in singles and doubles in Fort Worth, underlining the difficulty of qualifying in both disciplines.
"Of course I don't regret playing both," Pegula said. "We're used to playing both, but at the end of the year -- I don't know about her -- but I think it caught up with me. I keep telling myself that I had a great year. I don't think I've lost this many matches in the past three months."
Meanwhile, Sabalenka knew a straight-sets win would greatly improve her chances of advancement.
"I keep saying to myself, 'Just stay focused, keep fighting -- it doesn't matter, two or three sets, just get the win, the extra points,'" Sabalenka said. "At the end was a little pressure because you try to not think about this, but this thing stays in your mind. I'm happy that I was able to finish it in two sets.
"In the beginning, I said to my team that I'd prefer the second match to 100 percent know what I have to do to get through."