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Frannie Collin sunk League 2 Stevenage with an 87th-minute winner on an incredible night at the Gallagher Stadium.
Collin met a cross from substitute Ben Greenhalgh with a bullet header for his second goal of the night.
Stones will play Wrexham away in the second round.
Talk before the game was about Maidstone not conceding an early goal against their League 2 opponents.
The opposite happened in just the second minute as Alex Flisher headed Lee Worgan's clearance into the path of Jay May.
Boro keeper Chris Day could only parry May's strike and Collin reacted quickest to finish the loose ball by the post.
It was a dream start for a Stones side missing captain Steve Watt and, just like in the first game, Boro were given no time to settle.
They threatened after 18 minutes with Worgan making a brilliant low save Lee Barnard's header.
Worgan also kept out Roarie Deacon's useful first-time strike while Chris Whelpdale blasted over when through but generally Stevenage offered little.
At the other end Day was a nervous wreck - perhaps thinking he should have done better with May's shot for the goal - and United looked to play on his nerves with balls in the box.
He got away with one when referee Simon Hooper gave a free-kick when under pressure from May at Flisher's inswinging corner, otherwise Stones would have scored.
As it was, United's best chance of adding to their lead in the first half saw Flisher denied by Ronnie Henry as he ran on to Jack Parkinson's pinpoint pass.
Stevenage levelled two minutes into the second half with unmarked Darius Charles meeting a cross from Charlie Lee.
Maidstone looked rattled by the goal but cleared their heads and it took a smart block from Day to deny Coyle from Collin's pass.
Boro enjoyed more of the ball as the half wore on but Stones remained a threat on the break, particularly when they found Flisher.
Worgan blocked with his legs when Whelpdale went through and seconds later Maidstone had their winner.
Maidstone: Worgan, Simpson, Mills, Coyle, Miles, Rogers, Bodkin (Greenhalgh 78mins), Parkinson, May, Collin (Brown 89mins), Flisher. Subs not used: Jordan, Robertson, Davies, Kitt, Godmon.
Attendance: 2,226.