Melbourne Victory went down 2-1 to City in the Derby at Etihad Stadium on Saturday night.
A deflected effort from Bruce Kamau in the second half saw the home side beaten in the Hyundai A-League.
Leroy George had scored his first Victory goal to cancel out Marcin Budzinski's first-half opener for City.
But Kamau's goal in the 64th minute saw Victory suffer a second straight defeat to begin the season.
Victory made three changes to the starting XI edged by Sydney FC, with its trio of internationals – Mark Milligan, James Troisi and Kosta Barbarouses – returning.
Mitch Austin and Jai Ingham dropped to the bench and Leigh Broxham shifted from midfield to left-back, replacing Thomas Deng, while George moved to the wing.
In what was a lively start to proceedings, Lawrence Thomas was forced into two early saves to deny City forward Ross McCormack.
Victory looked energetic but lacked a final pass, with Troisi and Broxham both shooting over in the opening 25 minutes.
A deflected 30-yard drive from Milligan forced Eugene Galekovic into a save six minutes before half-time as Victory built into the clash.
But City opened the scoring on the stroke of the break, with Budzinski firing into the roof of the net from an angle.
However, Victory equalised just 10 minutes into the second half.
Troisi's pass released Barbarouses down the right and the New Zealand international crossed for George, who fired past Galekovic from an angle at the back post.
Victory almost took the lead just before the hour-mark, but Troisi's curling effort went just wide.
Thomas tipped over a McCormack free-kick before City regained the lead, Kamau's effort deflecting off Carl Valeri and over the Victory goalkeeper after a counter-attack.
Matias Sanchez came off the bench to make his Victory debut and the hosts pushed, with Rhys Williams' late header going over the bar before Thomas was needed to make a tremendous save from Budzinski.
Victory is away to Adelaide United in Round 3 on Friday night.
Hyundai A-League 2017/18 Round 2
Melbourne Victory 1 (Leroy George 55')
City 2 (Marcin Budzinski 45+3', Bruce Kamau 64')
Melbourne Victory: Thomas (gk), Broxham, Williams, Donachie, Geria, Valeri (c) (Ingham 82'), Milligan (Sanchez 76'), Troisi, George (Austin 70'), Berisha, Barbarouses
City: Galekovic (gk), Jamieson, La Rocca, Schenkeveld, Muscat, Jakobsen (c), Malik (Budzinski 43'), Kamau, Mauk, Fitzgerald, McCormack (Cahill 81')
Yellow cards: Valeri 1', Broxham 12', Williams 32', Fitzgerald 47', Muscat 56', Donachie 81'
Red cards: Nil
Venue: Etihad Stadium, Melbourne