Two early goals in two minutes gave City the perfect start, putting the hosts under pressure in the opening 10 minutes.
Dugandzic doubled City's lead two minutes later after latching on to a long Erik Paartalu pass and finishing skilfully to give John van 't Schip's side an impressive advantage.
The hosts were given several opportunities to respond but failed to test Andrew Redmayne in the City goal.
The home side's second-half substitution made the difference as Brandon Borrello's header gave Brisbane a lifeline, making the score 2-1 in the 66th minute.
Neither side were able to retain possession and capitalise on mistakes, with passes being poorly executed and tackles flying in from every angle.
The defeat sees Brisbane claim a new record as no team defending the title has ever started off the following campaign with four losses. This defeat ultimately sees them drop to the bottom of the table.
The win helps City climb the table to sixth with just five points recorded.