City have struggled without skipper Vincent Kompany and the Serbian's return added some assurance at the back.
The Tigers had the better of the opening exchanges, with Sone Aluko missing an early sitter and then Danny Graham having his superb finish ruled out for offside.
City were wobbling going into the break. Though having had more of the possession, Pellegrini's attack looked blunt with Edin Dzeko failing to impress.
The Chilean made the change instantly at halftime, hooking the Bosnian and replacing him with Alvaro Negredo.
The Spaniard immediately brought more purpose to City's attack and after missing an early chance, he headed the hosts in front on 65 minutes.
Bruce can be proud of his players on the day. Only Negredo's extra bit of class edged the game in City's favour.
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