The ninth seed beat Berdych 3-6 6-1 7-6(6) 6-2 in two hours and 47 minutes on Louis Armstrong Stadium.
Wawrinka, who has had to live in the shadow of compatriot Roger Federer back home, was blown off the court by Berdych in the first set, but in a match featuring superb ball striking and a combined 68 winners, Wawrinka's consistency proved the difference against the fifth-seeded Czech.
He closed out the match by breaking Berdych's serve for the sixth time to move into a quarter-final against Britain's defending champion Andy Murray or Russia's Denis Istomin.
"It's always tough to play against Tomas," Wawrinka said.
"He always puts you under pressure. I'm just really, really happy. Tonight is a night I will never forget."
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