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The hosts' best first half chance came after Jon Shaw blocked Paul Musselwhite's clearance, but City survived the scare.
The opening goal was scored 10 minutes into the second half after a lovely Tigers move. Stuart Elliott's ball forward was nodded on by Jamie Forrester to Ben Burgess who finished clinically from the edge of the area.
Forrester secured the win in the 69th minute. Chris Brass brought him down in the box, and the forward picked himself up to score the penalty.
City made it a professional job to comfortably hold on to the lead and run out 2-0 winners.
City line-up (4-4-2): Musselwhite; Hinds, Joseph, Delaney, Dawson; Price, Ashbee, Green, Elliott; Forrester (Holt 72), Burgess.
Un-used subs: Whittle, Thelwell, Keates, France.