Alistair Benson put the Tigers ahead just before half time. Ryan Williams completed the job 10 minutes into the second half after Clayton Donaldson flicked on Andy Holt's throw in and the winger ended the move by rounding the Darlington goalkeeper to score the second.
With five games of the Reserve season remaining, City sit on top of the Avon Insurance League First Division East table with a five point lead over second-placed Hartlepool. The next game is against Scunthorpe at Boothferry Park tomorrow, kicking off at 7pm.
City line-up: Musselwhite, Regan, Peat, Fry, Chapman, Holt, Heard, Russell, Donaldson, Benson, Williams.