After a delayed start, York raced into a two-goal lead against the hastily-arranged Blues, with a brace from Craig Atkin.
But the visitors rallied and a good passage of player characterised by neat passing culminated in skipper Dan Brown's 20-yard piledriver being pushed onto the crossbar by keeper Tommi Hird and Town's Ben Hogarth being bundled to the ground as he followed up.
The ball was picked up by the unfamiliar figure of assistant boss Danny MacGill who out-witted the City goalkeeper and slotted home Wanderers' first-ever competitive goal from the penalty spot.
The Seasiders then went on to look the stronger side and it was against the run of play when City added a third on the break through Amos Laverack who looked to be in an offside position.
But the young Whitby lads were undeterred and continued to move the ball around crisply.
One such move saw James Hall link up with Nick Trott, Nick Gurney, Hogarth and Rob Unsworth which ended up with a shot on goal held by Hird.
The Blues were knitting together well and pulled back a second goal when Hogarth fought back to dispossess a home defender, only to scuff a weak effort that the keeper somehow let trickle past him.
Half-time came at a bad time for the visitors who were now on top and spraying the ball around beautifully.
The powerful men in red went on to notch two more goals halfway through the second half, with their physical advantage proving the difference between the sides.
Tony Turner nodded home after Blues' keeper Rich Davies could only parry Laverack's header and Atkin completed his hat-trick from close range with around quarter of an hour remaining.
Davies, on his debut, picked up Whitby's man of the match award after making a string of excellent saves to keep his side in the game right until the final 15 minutes.
Wanderers: Davies, Hall, Danny MacGill, Darren MacGill, Brown (c), Trott, Gurney, Waring, Hogarth, Unsworth, Collins. Subs: Fox, Snaith.
Result: York City Supporters 5 Whitby Wanderers 2