Birmingham carved out their much-needed win after they had been reduced to only ten players after referee Rob Styles, who had an indifferent game, sent off Franck Queudrue for a tackle in the area on Benjani.
It was a controversial decision which brought the game to life. At the time Birmingham were leading 2-0 with the Zarate goals, but Elano converted the 56th minute penalty to put the game into the boiling pot.
It was another Styles decision which settled the game when he awarded a second penalty. This time he ruled that Sun had fouled Gary McSheffrey who rattled home 76th minute spot-kick to give Birmingham only their second win in 14 Premier League games.
Birmingham went into the game as if their lives depended upon the outcome. They laid siege on City for long spells in the first half and should have built up a more commanding lead than the single goal from Zarate.
But Sven-Goran Eriksson's Manchester City have recently run into the buffers. It was yet another disappointing performance on the road and it was only after Elano's penalty that they came to life.
Their best chance to go ahead occurred in the seventh minute when Elano put Benjani in possession. He shrugged off Radhi Jaidi only to see his shot smash against the post.
Shortly afterwards Jaidi saw his header cleared off the line by Javier Garrido, while the out of form McSheffrey carelessly blasted shot high over the bar.
Queudrue, recalled to the side after a two-month absence, did little wrong as a central defender replacement for the suspended Liam Ridgewell.
He even had an overhead kick brilliantly flipped over the bar by Manchester City's up and coming Joe Hart.
But the young keeper had little chance of preventing Zarate notching his second goal in successive games in the 40th minute. A direct pass by Queudrue was collected by Zarate, who calmly chipped the ball left-footed over the heat of Hart.
Against such lacklustre competition Birmingham were able to produce a smart attacking play and could have built up a more commanding lead.
Zarate produced the perfect finish when he scored with a low cross shot in the 54th minute only for Styles to send off Queudrue for a tackle on Benjani.
Elano slotted away the spot-kick, but Birmingham battled bravely and surprisingly won a penalty when Styles took centre stage when Sun Jihai knocked McSheffrey off the ball.
McSheffrey displayed no nerves as he slotted his spot kick past Hart to seal a much needed Birmingham win.