Graham Arnold's men travelled to AAMI Park under pressure after seeing both teams above them in the table - Perth Glory and Melbourne Victory - pick up three points apiece on Friday.
But they duly responded in kind, with Marc Janko's double enough to maintain their unbeaten A-League record this season and move them back level with City's neighbours Victory.
Janko opened the scoring early on when he beat Patrick Kisnorbo in the air at the back post and nodded beyond Andrew Redmayne.
Sydney perhaps got away lightly just a minute after Janko's first goal when goalkeeper Vedran Janjetovic appeared to foul City winger Damien Duff in the area, only for referee Kris Griffiths-Jones to give a free-kick against the veteran Irishman.
City tried hard to get back into the game but Janko sealed Sydney's win in the 83rd minute when he capitalised on an awful pass from Ron Wielaert and beat Redmayne again.
The hosts gave themselves a lifeline five minutes later when Erik Paartalu pulled one back with a header but, even after Sydney midfielder Milos Dimitrijevic was sent off for a second bookable offence in the closing stages, they were unable to force an equaliser.
Saturday's other A-League fixture saw the wait for a first top-flight win of the season for both Western Sydney Wanderers and Newcastle Jets go on, as the bottom two played out a 1-1 draw at Pirtek Stadium.
Tomi Juric put AFC Champions League winners Western Sydney ahead after 11 minutes, but the Jets hit back before the half-hour mark through a classy finish from Marcos Flores.
