The 25-year-old Japanese international recently rejoined the club he inspired to back-to-back Bundesliga titles, following an unsuccessful spell at Manchester United.
And with his every touch was greeted with cheers, he scored one and helped set up another in a 3-0 victory over Freiburg, before going off to a standing ovation.
"The fans have welcomed me back so warmly, and the reception before the game was fantastic," said Kagawa. "I had goosebumps throughout the entire game.
"I really wanted to win today and I'm glad we did. We have a wide range of qualify performers, and if we work well together, we can really be a force."
Coach Jurgen Klopp was delighted with Kagawa, who hobbled off with cramp just after the hour after seeing little action in recent months.
"He has already proved how influential he is," said Klopp. "It was a very, very good first game from him.
"So much has happened with him over the last few days. He has coped really well and produced a good performance.
"He has run himself into getting cramp. This is a good sign."
Midfielder Sebastian Kehl added: "Shinji is doing very, very well, especially with all the injury problems we have.
"It's also evident that he needs a bit of time to adapt. After 60 minutes, he was completely done. He will have to catch up to the pace."
