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.