Mitchell Duke's thumping 19th-minute header from Daniel Georgievski's cross proved enough for the Wanderers to claim their first victory over the Sky Blues since February 2017.
Markus Babbel's men attempted half the number of shots as their rivals and briefly looked to have succumbed to an equaliser in the second half.
Kosta Barbarouses met Brandon O'Neill's corner with a glancing header that bounced off the right post and appeared to dribble over the line, but the match officials waved play on and VAR (video assistant referee) decided against overruling the decision because of inconclusive replays.
Barbarouses let two chances go begging either side of that incident as the Wanderers held on for three points, thanks in part to Matthew Jurman's vital 94th-minute block on Milos Ninkovic.
Adelaide United earlier capped an excellent week by overturning a half-time deficit to win 2-1 at Newcastle Jets.
Riley McGree notched twice in 12 minutes against a club he played for on loan last year to hand head coach Gertjan Verbeek his maiden A-League victory three days on from the FFA Cup final triumph over Melbourne City.
Abdiel Arroyo's skilful volley had given Newcastle the lead, but the striker's inadvertent handball denied team-mate Matthew Ridenton a potential equaliser in the 69th minute and left the Jets winless.