The Wanderers showed great resolve to come from behind twice and snatch just their second win of a difficult season and first at Pirtek Stadium.
Goals to Safuwan Baharudin and then Aaron Mooy - either side of Mateo Poljak's first-half equaliser - looked to have City on track for a vital win in their chase for the finals.
But the Wanderers weren't done, first getting level through a Tomi Juric penalty before Rukavytsya struck in stoppage time.
The winning goal came after City's Connor Chapman had been sensationally sent off for manhandling referee Strebre Delovski.
