Mbwana Samatta pulled a goal back for Villa, but their wait for the club's first silverware since 1996 goes on as Pep Guardiola's men have now won six of the last seven major trophies in English football.
It mattered little as City had the luxury of recalling Aguero, Raheem Sterling and David Silva to the starting XI, and the gulf in class showed.
Guardiola's raft of changes also handed a rare start to Phil Foden and the 19-year-old more than justified his selection.
Rodrigo's fine pass picked out Foden to head back into the path of Aguero and the Argentine's deflected effort beat Orjan Nyland in the Villa goal to open the scoring on 20 minutes.
City doubled their lead as Gundogan's corner was met with a powerful downward header from Rodrigo.