Harriers blew a 2-0 lead at Vanarama National League rivals Boston United on Saturday, who forced a replay.
But this time Kiddy made no mistakes with their two-goal advantage and saw out the replay to progress.
“It was a very tough game on Saturday and you could see again tonight that with the new [Boston] manager coming in, they are trying to impress," said Gardiner.
“But I thought the guys were very professional and the gaffer is very happy with the way we managed the game.
"They have come out and performed and we had a clean sheet to boot.” Matt Gardiner
“We scored two good goals and could have had more, but we were really confident in moving the ball around.
“We could have done things a little bit better in some of the periods of play but, with everything that was asked of the players, they have come out and performed and we had a clean sheet to boot.”
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