The City defender played a full 90 minutes as the Swiss took a significant step towards qualification for the knockout stages with a 3-1 victory.
Goals from Kwadwo Duah and Michel Aebischer gave them a two-goal lead at half-time.
Barnabas Vargas pulled a goal back midway through the second half and Hungary pushed forward in search of an equaliser.
But Switzerland, with Akanji in the heart of their defence, stood firm from the late onslaught.
And they guaranteed the three points in injury time when Breel Embolo lobbed home the third.
Victory move Switzerland level with Germany on three points after the hosts thrashed Scotland 5-1 in the opening game of the tournament.
Akanji is the first City player to appear in this summer’s European Championship with 14 of our squad in Germany, more than any other Club.
