The German youngster, Chelsea's record signing, kept his composure as he latched on to Mason Mount's through pass and evaded goalkeeper Ederson before rolling the ball into an empty net in the 42nd minute to decide a tight encounter.
Premier League champions City were favourites ahead of the final but suffered a desperately disappointing night in their first Champions League showpiece match.
Despite winning three of the last four Premier League titles for City, Spaniard Guardiola failed to deliver the coveted European trophy he last won with Barcelona in 2011.
