The Steelmen were heading for defeat when they fell 4-0 down after 46 minutes to relegation-threatened Market Drayton Town in the Evo-Stik League South.
But Kinniburgh threw on Jake Bettles and he scored with his first touch and that was the catalyst for an incredible comeback.
Paul Malone scored the second, Bettles struck again to make it 4-3 and Phil Trainer’s superb flick brought them back on level terms.
And boss Kinniburgh felt the backing of a 400-plus crowd at Steel Park helped drive his team on once they get themselves back into the contest.
“For the first 30 minutes of the game I thought we were on top, we hit the bar and missed a couple of easy chances and we should have been two or three up,” the Steelmen manager said.
“Then we switch off and they get down the side with a quick free-kick and get a goal and we just capitulated for 15 minutes before half-time and we are 3-0 down, which didn’t reflect how the first half went.
“We came out in the second half, we organised everything at half-time and within 10 seconds we were 4-0 down.
“I am obviously a tactical genius in bringing Jake Bettles on! But you throw a couple of boys on in the hope that you are going to get something and when one of them scores with his first touch from the edge of the box, you start wondering if you might get something.
“And absolute credit to the boys because going forward we have done well.
“There was great character and great desire in a nothing game for us to come back and get the point.
“That was Market Drayton’s third game in five days so it’s really tough for them and they came and tried to sit and do their job.
“They were just knackered towards the end and we took advantage of that and credit to our boys for sticking at it.
“When you get towards the end of the season you need something to get you going.
“And if there hadn’t been over 400 people banging the boards and getting behind the boys, I don’t think we would have got back into it.
“So when you have that bit of atmosphere it really gets everybody going. You talk about the cliche of ‘the 12th man’ but I think ‘12th man’ really helped us through.”
Kinniburgh, meanwhile, insists youngster Dean McBride will bounce back from his error that gifted Market Drayton their fourth goal.
A big punt up the field from the kick-off at the start of the second half saw McBride attempt to head back to goalkeeper Dan Smith, only for his header to miss the stopper and roll into the net.
The defender was withdrawn soon after but Kinniburgh added: “With young Dean he is obviously disappointed with himself because of the fourth goal but the boy has not long turned 18 and he has been absolutely fantastic for us and he is doing a job week in, week out.
“There are going to be times when these young boys do drop below par and unfortunately for him it was today.
“I am half-glad because he has been doing so well for us, you are almost waiting for a fall to see how he reacts to come back.
“He will be back and we have a few games left with the academy as well as next week and he will react.”
Kinniburgh confirmed winger Dino Tuksar, who had come on as a substitute in the second half, suffered a dislocated shoulder after he was withdrawn late on in the game.