City took a deserved first-half lead through Alex Nicholls, as Tom Nichols showed great strength to hold up the play and lay the ball off to the midfielder, who finished into the top right-hand corner.
The visitors then doubled their lead nearly straight away as David Wheeler pounced onto Nicholls's rebounded shot, to simply finish into an empty net.
However, the home side got a goal back through former Tottenham Hotspur striker Jonathan Obika, who leathered a shot in from long range on the 65th minute.
Nathan Bryne almost made it 2-2 shortly after Obika's equaliser, as the midfielder's shot was deflected inches wide of the post.
Obika had two opportunities to bring the game level in the last 10 minutes of the game but could only direct both of his efforts into the stands.