Victory, without star Keisuke Honda, were on track to extend their superb run before Vidosic nodded home Scott Jamieson's desperate 92nd-minute cross.
Ola Toivonen had headed in Kosta Barbarouses' cross in the 55th minute on Saturday night to give Kevin Muscat's side the lead.
The result was a fair one given the weight of chances to City, and continued a Christmas tradition of late goals in the December derby.
Four of the nine derbies have featured game-changing goals in the 90th minute or later.
Honda joined fellow imports Raul Baena and Georg Niedermeier on the sidelines due to hamstring tightness and, with the Japanese star's absence, Victory started below their stunning early-season best in the first 45 minutes.
Honda's replacement Leigh Broxham put in the sort of shift that had kept him on Victory's books for 13 seasons, but there was a lack of fluency in midfield.
With a bleach-blond Luke Brattan working in overdrive, City rattled the champions and had most of the chances.
Each team missed a gilt-edged chance to take the lead, beginning with Victory's James Troisi.
The discarded Socceroo turned two City defenders after fine lead-up play from Carl Valeri, Toivonen and Leigh Broxham, but put his shot straight at Eugene Galekovic.
Rostyn Griffith, who earlier drew a terrific one-handed save out of Thomas, played in Lachlan Wales who raced clear of the Victory defence only to fluff his big moment with a heavy touch.
City skipper Scott Jamieson was at the heart of two comedy moments, heckling Troisi by making a 'call me' sign to reference national team boss Graham Arnold's failure to call the axed Socceroo.
