Alex Oxlade-Chamberlain's own goal rounded off a miserable night for Jurgen Klopp's men, who could have conceded many more in the second half.
Mohamed Salah struck the post and Sadio Mane headed wastefully wide as chances came and went for the visitors.
De Bruyne's 13th goal of the season came from the penalty spot on 25 minutes after Joe Gomez pulled Sterling to the ground.
But for the Brazilian goalkeeper and some wayward finishing, Liverpool could have been on the end of an embarrassing scoreline early in the second half as Gabriel Jesus fired straight at his international teammate, Sterling saw a shot deflected just wide and Virgil van Dijk cleared off the line from Foden.
But City more than laid down a marker and also showed why they are among the favourites to win the Champions League for the first time when European football returns in August.