A-League Wrap: Thompson hat-trick holds Sydney
The evergreen Thompson, 36, twice gave his side the lead at Etihad Stadium, only for Sydney to hit back quickly on each occasion through Marc Janko and Shane Smeltz.
Smeltz then put Sydney in front with 14 minutes remaining, but Thompson had the final word with a 79th-minute equaliser after fine work from Besart Berisha.
The Victory, who appeared lucky not to lose captain Mark Milligan for an early elbow on Terry Antonis, now trail leaders Perth Glory by three points, while Sydney are five points further back in fourth.
In Saturday's other game, Roy Krishna scored for the fourth match in a row to earn Wellington Phoenix a 1-1 draw at home to Central Coast Mariners.
Wellington dominated the opening exchanges, but fell behind shortly before half-time when Matt Simon pounced on a rebound after Glen Moss had fumbled a long-range shot from Nick Fitzgerald.
The hosts drew level in the 76th minute, a throughball from former Mariner Michael McGlinchey giving the in-form Krishna the chance to score again.