It was top v bottom in Group I, but the Swiss had to wait until four minutes into the second half when Cedric Itten finally broke the deadlock at the Stade de Tourbillon in Sion.
Itten - who will face City in the Champions League group stage for Young Boys - converted a right foot shot with former Arsenal skipper Grant Xhaka claiming an assist.
Though the hosts dominated much of the game - with Xherdan Shaqiri at the heart of most of Switzerland’s creativity – Andorra proved stubborn opposition in what was a sometimes niggly clash.
The tetchy nature of the game was highlighted when Akanji – rarely troubled in defence – was involved in a heated passage of play that ended with the City defender one of four players shown the yellow card.
Andorra tired in the closing stages and Xhaka sealed victory on 84 minutes with a long range effort to make it 2-0 before the impressive Shaqiri converted an added time penalty to make it 3-0 and give the scoreline a more emphatic look.
The win leaves Switzerland unbeaten in their six games to date.
