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.
Defender Yuichi Komano, whose missed penalty cost Japan a place in the World Cup quarter-finals, earned the biggest cheer of the night when he came off the bench in the 89th minute.
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.
Japan play Guatemala in Osaka on Tuesday when Zaccheroni will also be watching from the stands as he waits for his work permit to come through.
Thank you for reading 5 articles this month* Join now for unlimited access
Enjoy your first month for just £1 / $1 / €1
*Read 5 free articles per month without a subscription
Join now for unlimited access
Try first month for just £1 / $1 / €1