On 18 minutes an inswinging corner-kick from the right went into the Cray net with Steve King claiming the decisive touch at the near post.
Two minutes later the prolific Tony Stokes reacted when a deflection put the ball neatly into his path for a clip-shot over the head of the helpless Andy Walker.
Earlier in Cray's best attack Joe Vines had fired high over the bar, but it would be a night when the Wands got very little change out of the visiting defence.
Leigh Bremner and Paul Vines were tightly bottled up and became increasingly frustrated.
Michael Power tried to range deep and find space to make runs at the Concord defence, and when released on the left Tyrone Sterling looked capable of creating something for the Wands, but the visitors were relentless with their covering and tackling.
A flurry of Cray pressure midway through the second half saw Alex Stavrinou put a shot narrowly wide, and then the Cray midfielder saw a second shot take a deflection that looped the ball inches wide of goal, with the 'keeper beaten.
In the closing minutes Harry Elmes threaded a shot narrowly wide, but by then Concord had effectively shut up shop and the game was already won.
Cray: Walker, Burgess, Sterling, Day (Fray 72), Willy, J Vines, P Vines, Stavrinou, Bremner, Phillips, Power. Subs not used: Parkinson, Fasunan, Estrada, Hall.