Japan's playmaker, left out of the English champions' first three Premier League games this season, cut in from the left to unleash a fierce shot into the bottom corner five minutes into the second half, cancelling out Frank Acheampong's opener for a weakened Ghana side in Yokohama.
Yasuhito Endo, making his 136th appearance for Japan, put Samurai Blue in front in the 64th minute with a crisp, low drive before Keisuke Honda headed a third as 2010 FIFA World Cup™ quarter-finalists Ghana began to tire in rainy conditions.
Acheampong put the visitors in front against the run of play with a left-foot volley from the edge of the box which deflected off Atsuto Uchida and fizzed past goalkeeper Eiji Kawashima.
Ghana, who booked their place in the African qualifying play-offs for Brazil 2014 with a 2-1 win over Zambia last Friday before an 18-hour flight to the Far East, rode their luck until Kagawa's moment of magic.
Honda somehow missed an open goal and the busy Kagawa blasted just over as Japan, producing some neat one-touch football, pushed for an equaliser.
Japan, who have already secured their fifth successive FIFA World Cup appearance, were beaten 4-2 by a Luis Suarez-inspired Uruguay last month and failed to set pulses racing in a 3-0 win over Guatemala last week.
Alberto Zaccheroni's side lost all three of their games at the FIFA Confederations Cup in June but gained a measure of solace by winning the East Asian championship a month later.