Ippei Shinozuka's effort four minutes into the first half was all it took as Yokohama held firm for all three points in what was Postecoglou's first Cup match of the campaign.
The result places Yokohama at the top of Group A following Vegalta Sendai's 1-1 draw with Albirex Niigata, with five games remaining before the Cup enters the knockout phase.
Postecoglou, retaining his 4-3-3 formation, made six changes to the starting line-up that lost to Kashiwa Reysol last time out, with Yuzo Kurihara partnering Socceroos defender Milos Degenek in the heart of the defence, Takumi Shimohira deputising at left-back, Takahiro Ogihara, Kaina Yoshio and David Babunski occupying the midfield, and Ippei Shinozuka slotting in on the right wing.
Postecoglou's first victory, in front of his home fans at the Nippatsu Mitsuzawa Stadium no less, will come as a huge relief after his first two games in charge yielded a draw and a defeat.
Nevertheless, with Yokohama exhibiting a quick, upbeat style of football, confidence will be high ahead of Saturday's (AEDT) J1 League match against the winless Sagan Tosu.