Town registered a relatively straightforward victory from their first ever game against the Banbury-based club at Butlin Road on Bank Holiday Tuesday.
Rugby had had to wait until the final couple of minutes of the first half to take the lead through Justin Marsden though, but once Madundo Semahimbo doubled the advantage midway through the new period the result was never in doubt - with substitute Adam Shaw rounding off things at the death with a stunning finish.
The starting of scorers Marsden and Semahimbo represented two of three changes for Valley from their previous game ten days earlier at Lutterworth, with James Hancocks also back in after serving a one match suspension.
It was the visitors that were the first to threaten the goal though, when Elliot Barton's shot from the edge of the penalty was deflected wide by team-mate Levi Steele.
Harry Brock also put in a series of quickfire corners which troubled the hosts a little, before Town took control of proceedings and pinned Sports back into their own half for most of the remainder of the period.
Hancocks swung in a decent free-kick which Easington keeper Joe White did well to push away for a corner, and Barry Fitzharris fired one wide from distance as Rugby started to create chances of their own.
David Kolodynski lifted the ball over the bar from close range and then White did well to keep out Marsden's effort, with Caine Elliott also shooting wide of the target and Dan Summerfield's low strike being safely gathered by White.
The breakthrough came on 44 minutes when Kolodynski neatly set-up Marsden to fire home off the bar from a tight angle. Easington started the second half brightly again, with Steele drawing a good reaction stop from Ash Bodycote after he had been the first to pounce on Luke Swann's cross.
Rugby then survived back-to-back penalty appeals from the visitors, before they once more stepped up the gears to regain the initiative.
Fitzharris steered his shot wide, before Semahimbo snatched the vital second goal with a neck-twisting header to Danico Johnson's delivery into the box.
Shaw almost added a third just after his introduction from the bench when he seized upon defensive uncertainty between Brock and James Watts, with Easington defender Lloyd Sabin then doing well with a goalmouth clearing of a cross from another Valley sub Dylan Parker's first involvement in the game.
Shaw headed over a corner from Summerfield, before the forward grabbed his third goal of the month for his new club when he expertly lifted Josh Thomas's through ball over the head of the advancing White in the 90th minute.
Valley Line-up: Bodycote; Summerfield, Hancocks, Loyiso Recci, Clarke; Fitzharris, Elliott (Josh Thomas), Marsden (Parker); Semahimbo (Shaw), Danico Johnson, Kolodynski. Subs not used: Ahenkorah, Rosser. Booked: None.
Easington line-up: White, Barton, Brock, Fountain, Rose, Sabin, Swann, Watts, Steele, Moore, Walters. Subs: Eyre, Baldwin, Dunn, Butler.