Becker, of Germany, was upended by 6-foot-10 Croatian qualifier Ivo Karlovic 7-6 (7-5), 6-4.
Japan's Nishikori easily bested Croatian qualifier Franco Skugor 6-3, 6-2, advancing to the second round on the green clay courts of the River Oaks Country Club in Houston.
American James Blake, the 2008 Houston runner-up, was a winner after fighting back from a first-set loss to triumph over Argentina's Carlos Berlocq 6-7 (3-7), 6-3, 6-4.
U.S. wild card Ryan Sweeting downed fellow American qualifier Tim Smyczek 6-2, 6-2; Somdev Devvarman of India defeated American Robert Kendrick 6-2, 6-1; and Argentine Horacio Zeballos handled Ryan Harrison of the United States 6-4, 6-3.
Celebrity Families of 2014 [PHOTOS]