Southport 1-1 Stockport
Stockport suffered late heartbreak as a Sean Newton own goal denied them a first win in nine games.
County survived an early scare when Lewis King pulled off a brilliant parry to keep out a Lee Parry header.
And they took the lead when Danny Hattersley headed into the bottom right-hand corner from Newton's free-kick.
The visitors looked set for victory until Newton turned Karl Ledsham's cross into his own net with just five minutes left.