Paraguay have not qualified for the 2018 World Cup, but Japan will be in action this summer, with Akira Nishino's side opening their campaign against Colombia on June 19.
It was the South Americans that made the breakthrough in the 32nd minute when Oscar Romero converted following smart work from Antonio Bareiro in the final third of the field.
Kagawa turned on the style in the second period, however, as the Borussia Dortmund attacker twice set up Inui in the space of 12 second-half minutes to see Japan move 2-1 ahead.
Both of Inui's goals in Austria came from outside of the box, and Paraguay goalkeeper Alfredo Aguilar might well feel that he should have done better with the second effort.
Japan then scored a third in the 77th minute courtesy of an own goal from Santander, who turned a corner into the back of the Paraguay net.
That was not the end of the scoring in the international friendly, however, with Ortiz cutting the score to 3-2 in the final minute before the impressive Kagawa added a fourth for Japan moments later.
JAPAN (4-2-3-1): Higashiguchi (Nakamura 46'); G Sakai, Endo (H Sakai 46'), Ueda, Shoji; Muto (Osako 64'), Shibasaki; Kagawa, Okazaki (Haraguchi 74'), Yamaguchi; Inui (Usami 79')
PARAGUAY (4-4-2): Villar (Aguilar 12'); Benitez, Gomez (Valdez 56'), Balbuena, Alonso; O Romero (Sanabria 65'), Ortiz, Cardozo (Angel Romero), Sanchez (Mendieta 79'); Bareiro (A Romero), Santander