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A goal in the sixth minute of added time denied Maidstone a point in George Elokobi’s first game as their new manager.
Josh Shonibare gave United a second-half lead as they looked to end a run of 17 National League games without a win.
But the promotion-chasing Cards equalised through Padraig Amond and the same man scored their last-gasp winner.
Elokobi made three changes for his first official game in charge after a two-month stint as caretaker boss, including a first start of the season for defender Raphe Brown, following his recovery from ankle surgery.
Kevin Berkoe and Sol Wanjau-Smith also came into the side, with Jerome Binnom-Williams, Mark Marshall and James Alabi the players making way.
With Binnom-Williams on the bench, George Fowler captained the Stones for the first time.
Third-placed Woking enjoyed early possession while Maidstone looked to use the pace of Shonibare and Wanjau-Smith on the counter-attack.
That was no bad approach, for while the odd ball went out of play, Woking were quickly on the Stones whenever they tried to knock the ball around at the back.
Maidstone had several chances in a goalless first half.
The best came towards the end of the half with Regan Booty’s long ball releasing the lively Kevin Berkoe down the left.
He squared for Wanjau-Smith in a good position but Scott Cuthbert made an outstanding block.
Earlier, another Berkoe run led to shooting opportunities for Shonibare and then Dominic Odusanya, while Wanjau-Smith had an effort blocked after turning on Booty’s pass and Sam Bone fired wide at the far post from a corner.
Woking had a couple of big openings to break the deadlock among several half-chances in a goalless first half.
First, Mamadou Jobe cleared Amond’s effort off the line after Jim Kellermann kept the ball in play and squared.
Their other main moment saw Rhys Browne denied by an excellent low save from Dan Barden after making space for a shot in the box.
Cards keeper Will Jaaskelainen raced out of his area to halt Berkoe’s run on goal early in the second half, picking up a booking, with the free-kick coming to nothing.
But Maidstone were soon in again and this time they made it count with a lovely opening goal in the 58th minute.
Wanjau-Smith was the provider, going on a run down the left and playing a classy ball inside to pick out the run of Shonibare, who finished low past Jaaskelainen into the far corner.
Maidstone had looked reasonably comfortable before Woking’s 72nd-minute equaliser.
Amond was the scorer, squeezing a near-post header from a cross past Stones keeper Barden.
Maidstone, with deadline day loan signings Ryan Viggars and Ezio Touray both on for their debuts, tried to find a winner.
But Woking began to look more likely to score again, with Barden keeping out Kryan Lofthouse’s near-post strike before getting down well to deny substitute Marcus Dackers.
Seven minutes' injury time further fuelled the Cards charge and they took the points when Amond headed home a corner.
Maidstone: Barden, Brown (Binnom-Williams 81mins), Jobe, Bone, Fowler, Gurung, Booty, Odusanya, Berkoe, Shonibare (Touray 73mins), Wanjau-Smith (Viggars 66mins). Subs not used: Hadler, Alabi.
Woking: Jaaskelainen, Lofthouse, Casey, Cuthbert, McNerney, Amond, Moss (O’Connell 46mins), Browne (Wakefield 82mins), Nwabuokei (Dackers 69mins), Kellermann, Ince. Subs not used: Ross, Sass-Davies.
Referee: Ben Atkinson.
Attendance: 2,187 (432 away).