The Wands never really recovered from giving away a goal after just 71 seconds. They lost the ball on the halfway line and Hastings swiftly worked the ball upfield for Zac Attwood to fire past Andy Walker, with the Cray defence unable to cut out the danger.
Sean Ray nearly doubled the visitors' lead with a free header from a corner-kick.
Hastings 'keeper Daniel East came out to nick the ball away from Leigh Bremner, and then plucked out Jack Clark's dangerous cross after a surging run by Sam Long who has returned to the Wands from Margate.
Billy Burgess accidentally clattered East after the visiting 'keeper held a high ball that was dropping beneath the crossbar, but East recovered after treatment and was not much troubled between the posts as the big Hastings central defenders dominated the Cray forward line.
On 33 minutes Cray were punished for a clumsy tackle on United's new centre forward Elvis Hammond just outside the box. Lee Carey ripped the free-kick past the wall to beat Walker high to his left.
With little response coming from Cray after the break, Hastings continued to impose themselves physically on the game and went close on 61 minutes when Walker denied Attwood with a flying save.
On 81 minutes a comfortable win for Hastings was complete when Bailo Camara drove the ball into the net after his first shot was blocked.
Cray: Walker, Long, Pooley (Phillips 60), Saunders, Willy, Burgess, Estrada (Fray 46), Stavrinou, Bremner, Power, Clark. Subs not used: Fasunan, Hall, Abbott.
Cray travel to Whitehawk on Tuesday (7.45pm) then are at home to Leiston on Sunday 3 March (3pm).