Tigers boss Billy Russell included both Scott Wiseman and Russell Fry in a more experienced starting line-up than in the corresponding pre-season game, whereas Easington were without seven players who'd figured that night.
In perfect conditions and on a pitch that earned praise from the visitors, City served notice of their intent when James McGarry fired over after just 2 minutes.
And the Tigers went ahead four minutes later when Anderson seized on a misplaced clearance to score with a precise finish.
Easington responded well to the setback and matched their opponents with chances coming at both ends. Andy Graham passed up a free header from a Danny Medforth corner, only for City to break up field and Gary King was denied by Kev Appleyard's fine save.
The Eastenders' keeper then tipped an Ashley Allanson free kick over before it was City's turn to escape; Paul Wilkinson failing to convert from close range and Graham's shot from the resulting corner being cleared off the line.
Two minutes later Stuart Campbell produced an excellent goal-line clearance to deny Alistair Benson and the livewire City striker was thwarted for a second time by Appleyard's stunning reflex save.
Easington finished the half with a flourish and Craig Foster's header from another Medforth corner was hurriedly hacked away from danger.
If the first half had entertained a somewhat disappointing-sized crowd of 94, the second period proved even more compelling and, as City boss Billy Russell later acknowledged, it was the Eastenders who looked the likelier scorers. In the event the home side will reflect on three golden opportunities that weren't taken.
On the hour mark Jon-Paul Johnson – who along with the outstanding Neil Rutter had begun to dominate midfield – scuffed horribly wide with the goal seemingly gaping.
Ten minutes later Wilkinson cleverly teed up Brad Keyworth whose thumping drive was brilliantly turned away by goalkeeper Hall; Mike Nicholson eventually picked up the rebound and when he returned the ball to Keyworth just six yards out, the midfielder blasted high with a goal appearing certain.
As the visitors surprisingly tired, Easington finished the stronger but when Wilkinson failed to capitalise on a tremendous opening right at the death, their hopes went with it.
Despite the disappointment, this was a superb effort from Sean McLaughlin's side, a fact readily acknowledged by their opponents. Final mention must go to referee Sean Barber whose handling of the tie was near exemplary.
Easington: K Appleyard, N Rutter, S Campbell, JP Johnson, C Foster, A Graham, B Keyworth (M Hooley), D Medforth, P Wilkinson, I Barrow (D Mackay-Dundas), M Nicholson
Hull City: J Hall, T Mathews, T Briggs, R Fry, S Wiseman, M Byron, P Anderson, A Allanson, A Benson, J McGarry, G King (subs: C Russell, N Featherstone, W Atkinson, M Plummer, G Flounders)