With Sammy Clingan making his Sky Blue debut in midfield alongside Aron Gunnarsson it was City who went behind in the 39th minute to a goal from the Pars Andy Kirk.
Leon Best added some much needed muscle to the Sky Blues attack in the second half but the closest they came was when he hit the bar with a shot from inside the area.
The game finished on a sour note for Coventry when James McPake was carried off with what looked a nasty injury.
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