Play-off hopefuls Grays battled back from a goal behind early in the first half to upset John Coleman's team, for whom Gary Roberts had given them an early lead.
But two goals from Glenn Poole saw Grays go in front as they looked to spring a surprise.
Stanley battled back and Ian Craney levelled matters to set up an exciting final 25 minutes, but a goal from Aaron McLean with ten minutes remaining made sure Grays snatched victory in front of a crowd of more than 2,500.
Stanley started the better of the two sides and deserved Roberts' early goal.
On-loan Burton Albion striker Andy Todd supplied Roberts in the 18th minute and he didn't miss from close range, but Grays kept pressurising and, despite missing chances in the first half, they scored two goals in the space of five second-half minutes to leave the hosts reeling.
Poole was on fire and, after he had found the back of the net in the 58th minute, he then slotted home his second of the match soon after to give Grays the upper hand.
But Stanley hit back within two minutes after Craney's fierce shot levelled matters.
Then it was the turn of McLean who, with a smart finish, gave Mark Stimson's side the points.
Stanley can take solace in the fact they have been this year's runaway Conference leaders, but victory for Grays keeps them in with a shout of the play-offs.