Becker held off a pair of match points before defeating the fifth-seeded Wawrinka 3-6, 7-6 (7-5), 7-6 (7-5).
Wawrinka, world No. 12, paired with countryman Roger Federer to win an Olympic doubles gold medal two months ago in Beijing.
Sixth-seeded Russian Igor Andreev and eighth-seeded American Mardy Fish avoided upsets, as Andreev beat Austrian Jurgen Melzer 7-6 (7-5), 7-5 and Fish beat Argentine Agustin Calleri 7-6 (7-5), 6-2.
Also, Spaniard Feliciano Lopez beat Swiss wild card Marco Chiudinelli 7-6 (7-5), 7-6 (9-7).
This week's top seed is defending champion Federer, who captured a fifth straight U.S. Open last month for his 13th career major title. Federer begins play Tuesday against American Bobby Reynolds.
Gal Gadot cast as Wonder Woman for 'Batman vs. Superman'
Toddler uninjured after being knocked over by Obama family dog