The British number one dropped the first set on a tie-break but battled back to win 6-7 (1), 6-3, 7-5.
In doing so Konta became the first British woman to reach the last eight at Flushing Meadows since Jo Durie in 1983.
Konta had lost six of her previous seven matches with Pliskova, including twice on her home turf of Eastbourne, as well as in Nottingham and Birmingham.
None of those defeats will matter now with Konta continuing her fine season in the grand slams with a third successive appearance in a quarter-final.
It was a see-saw of a match, Konta holding two points for a double break in the first set, only to be pegged back and blown away in the tie-break.
Down a break in the second, a hold to love stopped the bleeding before three break points were engineered. Eight points in a row brought Konta level at 3-3 and another break had Pliskova suddenly feeling the heat.
At 5-3 two break points were saved, the first with a sensational forehand down the line, the second with a meaty volley, and when the Czech went long Konta levelled the match.
In a nip-and-tuck final set, Konta produced a gutsy hold to love for 5-5, and then broke to 15 to serve for the match.
One match point came and went, but when the second arrived and Pliskova's return floated out, Konta raised her arms in celebration.
"The key was to just keep going," she said. "You know with Karolina there will be massive portions of the match where I don't really know what I'm doing. I'm pleased to have played a great match.
"I've been in this position twice before here, so to go one step further is a massive achievement for me. Now I'm hoping to go two or three steps further."