The Spaniard beat Jordan Pickford with a 25-yard drive into the top corner to double City’s advantage after Sterling marked his 300th Premier League appearance with a clever finish from Joao Cancelo’s brilliant outside-of-the-foot pass.
Bernardo converted from six-yards to add gloss to the scoreline late on, as City moved back up to second in the table, three points behind leaders Chelsea.
In a one-sided affair, the defending champions created enough opportunities to win by an ever greater margin.
Pickford saved well to deny Bernardo and Cole Palmer, whilst Ilkay Gundogan hit the crossbar with a looping header and there was another let off for the visitors when VAR overturned a penalty decision after Sterling went down under the attentions of Michael Keane.
Watch the best bits from a dominant display in the video above.