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Jay May scored an injury-time winner at Hampton as Maidstone reached the FA Trophy first round on Saturday.
He finished Alex Flisher's knockdown from a Bobby-Joe Taylor cross to send Stones into Monday's draw.
United can count themselves fortunate to go through without a replay but the 1-0 specialists have done it again.
Hampton, seventh in the Ryman League Premier Division, were well on top in the first half.
They were first to most things, showed more urgency than Stones and should have been in front at the break.
They had two decent chances inside five minutes, Moussa Diarra losing his man at a free-kick but heading straight at Lee Worgan and Josh Casey caught in two minds whether to square or go for goal when well placed in the area.
Jamal Lowe and Dean Sinclair looked lively as Hampton continued to force the issue and on the rare occasions United did make inroads they came unstuck and looked vulnerable on the break, Worgan out sharply to deny Charlie Moone.
Stones’ first effort came after 24 minutes, Jack Paxman’s neat pass finding May whose 25-yard strike went well wide.
Player-coach Jamie Coyle urged United to raise their game and they looked a little better at the end of the half.
They might even have gone in front from the final action of the half, May heading over when unmarked from Taylor’s free-kick.
Hampton made the better start after the break but home keeper Mark Smith was forced into a flying save from Taylor’s 30-yard free-kick after a foul on Callum Driver.
Stones started to keep the ball better and when May, Healy, Matt Bodkin and Adam Birchall worked an opening for down the right for Taylor, Smith could only parry his cross and substitute James Rogers sent the loose ball over.
Maidstone turned to Alex Akrofi with just over 20 minutes left and within seconds he was denied by the outstretched leg of Smith when played in by Taylor.
Hampton’s Casey and Healy for Stones had efforts blocked in the last 10 minutes.
Taylor then flashed a strike inches wide in the final minute of normal time.
Just when a replay looked certain, May met Flisher's header to win it for Stones.
Maidstone: Worgan, Driver, Mills, Coyle, Parry, Paxman (Rogers 54mins), Bodkin (Flisher 76mins), Healy, May, Birchall (Akrofi 69mins), Taylor. Subs not used: Banya, Collin.
Attendance: 482