Baker's spot-kick cancelled out Rickie Lambert's penalty in first-half stoppage time to deny Southampton their first win of the season.
Stockport had the first attempt on goal, but Baker shot wide after Peter Thompson's lay-off.
Lambert went close with a free-kick from 25-yards, before Danny Pilkington called Southampton stopper Kelvin Davis into the first save of the match.
Referee Carl Boyson spotted a handball following Adam Lallana's corner on the stroke of half time and Lambert made no mistake from the spot.
In the second half Southampton began to dominate and Lambert, Lloyd James and Wayne Thomas all spurned opportunities to double the advantage.
And they were made to pay in stoppage time when Boyson again pointed to the spot after Thompson's shot was handled giving Baker the chance give to earn County a point - one he did not pass up.