Eibar's Inui had set up the victory with two second-half goals, both assisted by Borussia Dortmund's Kagawa, after Oscar Romero had given the South Americans a 32nd-minute lead.
Richard Ortiz pulled one back for Paraguay on 90 minutes before Kagawa crowned an influential performance with Japan's fourth a minute later.
The result ensured a bright finish to Japan's preparation for the World Cup in Russia, following 2-0 defeats to both Switzerland and Ghana.
They open their campaign in Group H on June 19 against another South American side, Colombia, in Saransk before taking on Senegal and Poland.
(Reporting by Neville Dalton; Editing by Christian Radnedge)