Nishikori advances to Memphis quarter-finals
File picture shows Kei Nishikori of Japan in action against Frank Dancevic of Canada during the Davis Cup tennis 2014 World group first round in Tokyo on February 2, 2014 - by Toshifumi Kitamura
Nishikori, a top seed for the first time in an ATP event, led 4-2 in the second set but was broken in the eighth game by Becker to level the set.
But the German double-faulted away a break in the ninth game and Nishikori held for the victory after 84 minutes.
The 17th-ranked Japanese star denied Becker on 5-of-8 break points while winning the same amount of break chances from the German.
Nishikori, who like all top-four seeds enjoyed a first-round bye, also connected on 65 percent of his first serves to 48 percent for Becker.
Nishikori, who scored three points to lead Japan over Canada in a Davis Cup tie earlier this month, reached a last-eight matchup Friday against Russian Alex Bogomolov, who defeated American Ryan Harrison 6-3, 2-6, 6-2 in another second-round match Wednesday.
Also reaching the quarter-finals were Americans Jack Sock, who bounced Czech Jiri Vesely 6-2, 6-1, and Michael Russell, who ousted countryman Tim Smyczek 6-2, 7-6 (7/5).
Russell will next face the winner of a Tuesday matchup between Australian third seed Lleyton Hewitt and Cypriot wildcard Marcos Baghdatis.
Either Spanish second seed Feliciano Lopez or Croatia's Ivo Karlovic will face Sock in the quarter-finals.
US qualifier Denis Kudla beat compatriot Donald Young 6-1, 6-1 to book a second-round match Thursday against Taiwan fourth seed Lu Yen-Hsun.