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Jerome Binnom-Williams scored an injury-time equaliser as Maidstone halted their nine-match losing streak.
Sha’mar Lawson gave the National League’s bottom side a deserved half-time lead at Yeovil.
Substitute Alex Fisher levelled, followed by a Sam Bone goal own goal, as Yeovil turned the tables midway through the second half.
But Maidstone avoided a 10th successive defeat when skipper Binnom-Williams headed home in added time.
Jack Cawley made his first start since September in place of the injured Ryan Galvin, as Maidstone made one change to the side beaten at Torquay.
Cawley lined up on the left of a back three alongside Bone and Mamadou Jobe and United were untroubled in the first half.
The Stones were nice and bright in possession, popping the ball about with purpose and keeping it pretty much exclusively on the deck.
Yeovil, on the other hand, seemed to keep the ball for the sake of it.
They’d knock it across the back line and into midfield for a spell and soon have the crowd on their backs, urging them to get it forward.
They perhaps a point at times but Maidstone set up well out of possession and deserved credit for denying them anywhere to go.
The opening goal, in the 20th minute, showed the football Maidstone are capable of playing, with Roarie Deacon and Jobe combining superbly on the left to tee up Lawson, who finished neatly into the bottom corner from around the edge of the box.
Andrew Oluwabori fired wide as Yeovil tried to make some progress but it was their only sight on goal in the opening 45 and they were booed off at the break.
Yeovil boss Mark Cooper made a double in a bid to shake things up.
They had more purpose about them, with Matt Worthington’s run and cross to the back post eluding one of the substitutes, Fisher.
Sam Corne went close to a second for Maidstone with a deflected strike from the edge of the area.
But Yeovil’s improvement saw them turn the game around with two goals in three minutes.
The equaliser came in the 67th minute, Fisher meeting Morgan Williams’ cross to the back post with a smart half-volley into the opposite corner.
And with Yeovil’s tails up, unfortunate Stones defender Bone diverted the ball into his own net as he tried to cut out Worthington’s 70th-minute cross.
The game was in the first of five added minutes when the visitors equalised.
Skipper Binnom-Williams was the scorer with a header from George Fowler’s deep free-kick.
Yeovil: Smith, Williams, Richards-Everton (Johnson 46mins, Wakefield 76mins), Worthington, D’Ath, Maguire-Drew, Cooper, Oluwabori, Clarke (Fisher 46mins). Staunton, Agbaje. Subs not used: Young, Buse.
Maidstone: Barden, Fowler, Jobe, Bone, Cawley (Pattisson 68mins), Binnom-Williams, Deacon, Booty, (Ghandour 58mins), Corne, Lawson Barham. Subs not used: Alabi, Mersin, Jeche.
Referee: Adrian Quelch.
Attendance: 2,421 (164 away).