Despite playing much of the contest on the back foot, Puig played the more assured tennis when it mattered to run out a 1-6, 6-4, 6-4 winner.
"It was difficult conditions today - the conditions were heavy and the roof was open this time - so it took me a little bit of time to adjust," Puig said. "I just kept fighting and that's what got me through today."
Tough fight today but happy to get through and spend some time taking selfies with everyone!!! ????? pic.twitter.com/wBLmuWXlpY
Puig, who also beat Kvitova on her way to Olympic gold this summer, has now won all four of her encounters with left-handers in 2016. "I didn't know I hadn't lost [to a left-hander], but they're very difficult to play and always tricky," she said when quizzed on her impressive record after the match.
The result will smart for Kvitova, who led 4-2 in the decider and came within a point of moving 5-3 ahead. However, from 40-15 down Puig produced the most impressive of turnarounds; a fizzing forehand return winner and a backhand onto the baseline bringing her to deuce, before breaking when a frustrated Kvitova sent a forehand long.
Elsewhere, wildcard Naomi Osaka delighted the crowd by knocking out No.6 seed Dominika Cibulkova to reach her third WTA quarterfinal and first at a Premier event. Unleashing serves regularly in excess of 120mph and attacking anything remotely short, Osaka recovered from the loss of the first two games to romp home, 6-2, 6-1, and register just the third Top 20 win of her career.