Both teams won their opening fixture 4-0 and remained committed to scoring goals in an engaging display of attacking football.
Silva benefited from Jussi Jaaskelainen's goalkeeping error in the 26th minute to give City the lead before Barry doubled the advantage with a long-range effort in the 37th.
However, Ivan Klasnic immediately responded to give Bolton hope, but Dzeko's early second-half strike restored City's two-goal cushion.
Kevin Davies again breathed life into Bolton's afternoon as he headed home Paul Robinson's delivery in the 63rd, but the hosts couldn't pull off a further comeback.
A 3-2 win for Manchester City against Bolton
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