The Reds could have drawn level with Sydney in second place in the table with a victory but were firmly out of the contest even before Jordan Elsey was sent off with 63 minutes played.
Adam Le Fondre's superb header from Rhyan Grant's cross put the visitors ahead at Coopers Stadium after just six minutes, and the experienced striker spurned a good chance for a second before the break.
Stefan Mauk hit the post for Adelaide early in the second half and Le Fondre compounded their frustrations two minutes later, burying his second after James Delianov had denied Kosta Barbarouses.
Le Fondre then turned provider, crossing low from the right to present Bobo with a simple finish, the goal given after a VAR (video assistant referee) review saw an initial offside call correctly overturned.
Elsey, who was arguably fortunate to receive only a yellow card for a two-footed tackle on Bobo in the first half, earned his second booking when he brought down Anthony Caceres.
Teenager Patrick Wood scored a minute after coming off the bench after a positive run, with Yaya Dukuly's first A-League goal at the end of a slick move providing little consolation to Adelaide, who saw an eight-game home unbeaten run come to an end.
Sydney is now four points behind leader Melbourne City, having played a game more.