The 17 million pound ($27 million) signing from Borussia Dortmund, touched in from close-range to score United's second goal in a 3-2 victory over Fulham on his first appearance at Old Trafford.
"Kagawa played the central role in United's offence when Wayne Rooney was left out," the Sports Nippon daily said, reporting on the Japanese international's appearance on its front page.
"Kagawa became the star in the Theatre of Dreams -- Old Trafford!" said the Nikkan Sports tabloid.
Kagawa told Japanese media after the match that United, last year's Premier League runners-up, demanded a high level of performance, telling Jiji Press he was confident he could live up to expectations.
United's victory over Fulham was overshadowed by an injury to Wayne Rooney, which left the England striker with blood streaming from a deep gash in his thigh after he was caught by Hugo Rodallega.
But manager Sir Alex Ferguson is hopeful that Kagawa and Robin van Persie, a 24 million pound capture from Arsenal, who also scored on Saturday, can prove more than adequate replacements.
Ferguson believes their partnership showed enough promising signs to hint at better things to come and said: "It was fine. There will be a better understanding as time goes on but I was pleased with that."