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At age 22, Puig became Puerto Rico's first Olympic gold medallist with a stunning performance.
The Canadian teen had earlier stunned third seed and defending champion Naomi Osaka.
The former world number one was going through a low phase in her career when an interactive session with a Keralite yoga expert revived her fortunes.
Top seed Ash Barty became the first Australian woman to reach the Wimbledon singles final for 41 years.
In the first all-Australian women's Grand Slam quarterfinal since the 1980 Wimbledon championships, the 25-year-old Barty produced a calm and composed display on Centre Court.
Kerber's poor record at the French Open got no help when the German was knocked out in the first round by Ukrainian qualifier Anhelina Kalinina.
Brady produced a fearless brand of tennis to down 2016 champion Kerber 6-1, 6-4.
The 32-year-old has not won a title since picking up her third Grand Slam at Wimbledon in 2018 under then coach Wim Fissette.
Kerber's second-round exit is her worst Wimbledon result since 2013 and follows a first-round exit at the French Open in May.
Kerber began her title defence by surviving a battle of wits at Wimbledon as she beat fellow German Tatjana Maria on Centre Court.