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Jay May's penalty and an injury-time strike by Bobby-Joe Taylor saw Maidstone reach the FA Cup first round for the second year running.
May later had a second penalty saved against a Chippenham side who finished Saturday's tie with nine men, Conor McCormack injured after all three substitutions had been made and captain Greg Tindle sent off.
Substitute Taylor made sure of victory at the end of seven minutes' injury time.
Chippenham, third in the Southern League, made a bright start and when Jamie Coyle’s loose backpass led to a corner which Stones struggled to clear, Scott Bevan’s 20-yard half-volley brought a smart low save from Lee Worgan.
Tom Mills worked home keeper Kent Kauppinen after exchanging passes with Matt Bodkin but early on it was difficult for Stones to impose themselves against the hardworking hosts.
That changed midway through the half as Jay Saunders’ men started to get on the ball, Bodkin combining neatly with Jack Paxman and breaking into the box only to see his strike forced out for a corner.
Chippenham remained a threat but United perhaps should have taken the lead on the half-hour, Manny Parry losing his man from Bodkin’s free-kick but heading over.
Sandell might have done more with a header for the hosts before United went in front.
The goal came on 40 minutes with May sending Kauppinen the wrong way from the penalty spot after Alex Osborn was tripped just inside the area meeting a Bodkin centre.
Stones were comfortably the better side playing up a 6ft slope just after the break, although the hosts were unhappy at the number of free-kicks going their way.
May got plenty on a header from another Bodkin cross but sent it straight at the keeper, a decent chance for a second goal.
Ian Harvey dragged an effort wide and Ryan Campbell flashed a strike across the face of goal - any touch and it would have been in - as Chippenham rallied.
United lost Callum Driver to injury midway through the half which meant a reshuffle in defence, substitute Steve Watt partnering Parry with Coyle switching to right-back.
A mad couple of minutes followed as May had a controversial penalty saved.
There was no doubt he was taken down by Kaupinnen but the foul came after he’d pushed a shot wide when played in by Joe Healy.
That came on 77 minutes and soon after Chippenham were down to nine men with last man Tindle dismissed for bringing down Osborn on the edge of the area.
There were a few nervy moments as Chippenham put balls into the Maidstone box late on, Watt with a goalline block from Oli Taylor.
Substitute Taylor clinched victory when played in by May, jinking his way past several players before finishing.
Maidstone: Worgan, Driver (Watt 66mins), Mills, Coyle, Parry, Paxman (Rogers 68mins), Bodkin, Healy, May, Birchall, Osborn (Taylor 82mins). Subs not used: Collin, Akrofi, Bridle-Card, Flisher.
Attendance: 811.