Roberto Mancini's side trailed to Steven Caulker's 21st-minute opener but drew level through Sergio Aguero in the second half before Dzeko struck late on to close the gap on leaders Manchester United to two points.
The visitors successfully marshalled City's attacking players in the opening stages at the Etihad Stadium and went ahead in the 21st minute when Caulker met Tom Huddlestone's free-kick with a header that Joe Hart fumbled over the line.
Huddlestone came within inches of extending the visitors' lead with a crisp drive, but City felt they should have been awarded penalties for an apparent William Gallas handball and a block by Huddlestone on Pablo Zabaleta.
Carlos Tevez and Zabaleta both tested Spurs goalkeeper Brad Friedel in the minutes prior to half-time, before Aguero drew the hosts level in the 65th minute.
David Silva's pass was inadvertently diverted into Aguero's path by a Spurs player and the Argentine cut inside Caulker before rolling the ball past Friedel.
Silva shot wide and Friedel saved well from Aguero, but victory looked set to elude the home side until Silva picked out Dzeko with a chipped pass and the Bosnian hooked a left-foot half-volley into the roof of the net.
Chelsea, who began the day in second place, can cut United's lead to a point if they win at home to Liverpool later on Sunday, while Newcastle United are also in action at home to West Ham United.
Source: AFP
Source: AFP