Kawasaki midfielder Kengo Nakamura sent a pass through to Kagawa, whose shot from just outside the area went in off the post in the 64th minute.
Japan set the early pace with CSKA Moscow midfielder Keisuke Honda and Yuzo Kurihara threatening the South Americans' goal.
The visitors turned the momentum round after 15 minutes, but the trio of forwards Nestor Camacho, Lucas Barrios and Roque Santa Cruz failed to find the net.
Japan had a good chance in first-half injury time when skipper Yuji Nakazawa's header from Nakamura's corner was saved by Justo Villar.
Paraguay midfielder Jonathan Santana's sizzling shot narrowly went wide at the beginning of the second half and he mishit a similar shot 10 minutes later before the home side scored the opener.
The visitors had a chance to level, but defender Paulo Da Silva's header from a corner was cleared by Nakamura in the 84th minute.
Japan's new Italian coach Alberto Zaccheroni watched the game from the stands as he has yet to obtain a work visa. His first stint will be friendlies in October against Argentina at home and Korea Republic away.