In the reverse fixture against Bournemouth in November, the Black Cats found themselves 2-0 down inside 15 minutes at the Stadium of Light before fighting back to win 3-2.
But Regis Le Bris' side got off to a brighter start on the south coast, with Noah Sadiki's low shot forcing a fine save by Petrovic, while they also had an early penalty appeal waved away by referee Gillett.
And after soaking up a period of pressure by Bournemouth, the visitors took the lead through Eliezer Mayenda's first league goal since the opening day of the season.