Jason Oswell and Darren Stephenson had put County 2-0 ahead in the all National League North battle at Aggborough.
But Fraser Horsfall - who later saw red for two bookings - and Emmanuel Sonupe scored for Harriers to ensure the 1987 Trophy winners remain in the hat.
Sonupe also saw a spot kick saved by Stockport keeper Ian Ormson but Kiddy boss Eustace was pleased with a replay.
“We drew, we showed great character and are happy with the result overall,” Eustace said.
“Stockport are a very, very tough team. They are a difficult team to break down but we created a lot of chances.
“To go 2-0 down so early in the second half was tough but we showed great spirit and togetherness. I’m happy the lads got a draw in the end.
“To come back from two goals down against one of the top sides in the division shows that the group is getting stronger and stronger.”
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