Serving for the match at 5-4 in the second set, Brengle appeared to be easing across the finishing line. However, staring down the barrel of defeat, Kvitova was suddenly liberated, unleashing some carefree strokes to recover from 0-40 down and get back on serve.
In the subsequent tie-break Kvitova dug a hole that there was no way out from, Brengle building a commanding lead before snapping a backhand passing shot to complete a 6-3, 7-6(2) win - her first over a member of the Top 10.
Kvitova, meanwhile, will have to regroup ahead of her next outing in Madrid. After missing Indian Wells and Miami due to exhaustion, the Czech's only competitive tennis since mid-February were a couple of singles outings whilst on Fed Cup duty.
This rustiness was evident in the statistics, with Kvitova's impressive tally of 39 winners undermined by the same number of unforced errors.
"I think that Madison played a solid match. She didn't miss much and it was really difficult for me because when I had the opportunity for winners I missed," Kvitova said. "The confidence wasn't really high then and I didn't feel physically there as well.
"I mean I was still tired probably from the Fed Cup. And on the clay you need to be physically ready for it. So, that was one of the reasons as well. I need to be still patient and I'm looking forward to next week which I'm going to use to practice on clay."
In contrast, Brengle coughed up a miserly 13 errors. The American's reward for this disciplined display is a quarterfinal - her first at a Premier event - against WTA Rising Star Caroline Garcia after she defeated wildcard Carina Witthoeft, 7-6(4), 6-2.