The Cote d'Ivoire international was chosen on the right side of attack ahead of Burkina Faso's Bertrand Traore, with summer signing Moussa Dembele also settling for a spot on the bench.
Bruno Genesio's side headed to the Etihad in a poor state, having failed to kick on from their decent 2017-18 campaign.
Thoughts of a terrible outing in England were doused after Cornet benefitted from a Fabian Delph shambolic defending, off Nabil Fekir's cross, to curl the opener past goalkeeper Ederson in the 26th minute
Just before the interval, Skipper Fekir doubled the visitors’ lead after Memphis Depay picked City's pocket in their half.
In the 67th minute, the Citizens pulled one back through Bernardo Silva with substitute Leroy Sane doing all the hard work.
There was time for Riyad Mahrez to make his Champions League debut for City, but the former Leicester City wing wizard could do little to avert Lyon's first-half damages.
Traore was brought on in the stoppage time for Cornet, who delivered a Man-of-the-Match performance as Lyon go top of Group F.