With new Japan coach Alberto Zaccheroni watching from the stands, Kagawa's clinical 64th-minute finish proved the difference in front of 65,000 fans in Yokohama.
"The movement was excellent," Italian Zaccheroni told reporters. "I saw Japan at the World Cup and they were as good as I expected. Let's hope it continues when I coach them."
Kagawa added: "We lost to them at the World Cup so it's good that we got some payback. It was nice to score in front of the new coach."
Paraguay had beaten the Blue Samurai on penalties in the last 16 of the World Cup in South Africa after a scoreless 120 minutes and Saturday's encounter had a similar feel until Kagawa broke the deadlock.
Paraguay almost equalised three minutes after Kagawa's strike, Luca Barrios - Kagawa's Dortmund team-mate - superbly denied by Japan goalkeeper Eiji Kawashima after breaking clear.
