Two metre tall Anderson hurled down 22 aces, the last one on match point, to send Wawrinka spinning to his first loss since he beat world number one Novak Djokovic in spellbinding fashion in the Roland Garros final earlier this month.
Anderson, the world number 17, now has four consecutive wins against Wawrinka, the first of that sequence being the Swiss's first loss after he won the 2014 Australian Open.
"That's a funny coincidence," Anderson, who is in the process of taking out duel U.S. citizenship, told reporters after moving into the quarter-finals.
"I've just played these guys a lot of times, and I think it gives me confidence, knowing the guy I beat today just won the French Open and I watched him playing and beat the best players in the world doing it.
"A lot of things I have worked on came to fruition today."
Wawrinka, the second seed at the prestigious Wimbledon curtain-raiser who needed only 49 minutes to beat Nick Kyrgios on Tuesday, did not play badly.
But even his lethal backhand could make no impression on the mighty Anderson serve.
He fought hard, saving five match points and he missed a golden opportunity to win the second set before succumbing.
Wawrinka will rue the few chances that went begging on a cloudy day in west London, especially the two set points he had on the Anderson serve at 6-5 in the opening set, and the two in a drawn-out second set tiebreak, the second of which he squandered at 11-10 when he sprayed a forehand wide with the court at his mercy.
Seventh seeded Frenchman Gilles Simon earlier beat Australian teenager Thanasi Kokkinakis 6-4 6-2 despite losing the first nine points of the match.
Simon will face Milos Raonic in the quarter-finals after the Canadian third seed beat Richard Gasquet 6-4 6-7(5) 6-1.
Anderson awaits the winners of Spain's Guillermo Garcia-Lopez or Rafa Nadal's conqueror Alexandr Dolgopolov.
Top seed Andy Murray was not in singles action on Wednesday. He will face Fernando Verdasco on Thursday.
(Editing by Pritha Sarkar)
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