The 33-year-old Massaro, who last month became the first female English player since 1951 to lift two British Open titles, hit consistent lines to go two games to the good, with her dominance on the backhand side in particular, seeing her seize the initiative against an out of sorts King, who hit a number of errors early on.
A drop in intensity from the Lancashire ace saw King come back to take the third.
But Massaro fought back from game-ball down in the fourth to seal an 11-7 11-8 5-11 13-11 victory in 50 minutes.
“The fourth was really close and I felt like I had pulled away a bit,” said Massaro.
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“But then she ended up coming back really well and I was in a little bit of a battle really.
“It’s quite hot on there and it’s quite bouncy being on a plaster court.
“I think I started quite well. Joelle was a little bit off at the beginning but she began to up her game a little bit.
“I felt like she started hitting to my forehand a little bit more and was keeping it off my backhand.
“It took me a little while to rejig my plan a little bit and try and figure that out.
“I was perhaps a little bit edgy towards the end more than anything, it was a tough draw for me to play her in the last 16 on a plaster court.”
Massaro will take on either World No.4 Raneem El Welily or United States No.2 Olivia Blatchford in the last eight.