Iyseden Christie headed home Gareth Seddon's cross in the third minute of stoppage time to seal a famous comeback after the Poppies had the odds stacked against them.
It turned out to be a farcical afternoon as referee Ray Lee decided to take centre stage by dishing out 10 cards including a red one for Tommy Jaszczun in the first half.
The Poppies fell behind after just five minutes when Charlie Griffin fired home after capitalising on a mistake from Guy Branston.
But Kettering stormed into the game and Iyseden Christie forced James Bittner into a fine save before Darren Wrack had a goal bizarrely ruled out for offside.
The game's crucial point came two minutes before the break when Jaszczun was handed his marching orders after a tussle with Griffin turned ugly.
Quite why the striker didn't follow as well, only Mr Lee will know.
In fact the referee continued to lose control in the second half and even Jean-Paul Marna was booked before he entered the pitch as a substitute.
However, the Poppies poured forward in search of an equaliser and it came on 75 minutes when John Dempster fired home after Exodus Geohaghon's header had been parried by Bittner.
Marna shot wide late on as both sides searched for a winner but it was Christie who stole the show in the dying moments.
Salisbury: Bittner; Clohessy, Cook, Sangare (sub Beavan, 24 mins), Robinson; Dutton, Turk (sub Davies, 81 mins), Clarke, Feeney (sub Herring, 81 mins); Tubbs, Griffin.
Poppies: Harper; Dempster, Geohaghon, Branston, Jaszczun; Eaden (sub Potter, 53 mins), Boucaud, Wrack, Westcarr (sub Seddon, 73 mins); Beardsley (sub Marna, 58 mins), Christie.
Referee: Ray Lee.
Goals: Griffin (5 mins, 1-0), Dempster (75 mins, 1-1), Christie (90 mins, 1-2).
Cards: Branston, Tubbs, Griffin, Clohessy, Eaden, Marna, Potter, Clarke, Robinson (all yellow), Jaszczun (red).
Attendance: 1,191.
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