Dudfield set up City's second as well, crossing for Appleby whose header hit a defender, but the midfielder got to the rebound to put City 2-0 up 5 minutes before half time.
Early in the second half City had a third chalked off by the referee. Stuart Green ran through the Scarborough defence before putting the ball past the 'keeper, but the referee brought back play for a foul on Green rather than playing the clear advantage.
However, there were no complaints when Green scored from Gary Alexander's through ball 20 minutes from time to make it 3-0.
Minutes later Rennison headed home a corner to pull one back for the home side, but there was to be no way back, and City even had time to have another goal disallowed when Elliott was denied his second of the night by the linesman.
City will take a team to Selby Town tomorrow evening, expected to be made up of reserves and juniors who did not appear at the McCain Stadium tonight.
Starting line-up (4-3-3): Glennon; Edwards (Greaves), Anderson, Strong, Smith; Green (Williams), Ashbee, Appleby (Price); Dudfield, Alexander, Elliott (Peat).
Un-used subs: Musselwhite, Whittle, Philpott.