The Hatters went into the game unbeaten in five league games and completely dominated the opening exchanges.
But it was Southend who created the first opening, with winger Kevin Betsy charging down the right flank before unleashing a tame effort at goalkeeper Fraser Forster, who was making his league debut.
Forster then denied Jean-Francois Christophe after he was teed up by Betsy, while at the other end striker Anthony Pilkington bent a 25-yard free-kick round the Shrimpers' wall and inches wide of the post.
But Blues took the lead straight from Adam Federici's goal kick. He thumped the ball down the centre, Alex Revell flicked the ball on and Barnard turned Jaroslaw Fojut and then fired past a helpless Forster.
The Hatters had to wait until 33 minutes for their first shot on target, but Tommy Rowe's effort was straight at Federici.
Stephen Gleeson fired wide from distance for County, before Forster did well to turn a curling left-footed shot from Hal Robson-Kanu out for a corner on the stroke of half-time.
Stockport started the second half with some bright football and were nearly rewarded when Jim McNulty's cross from the left was flicked goalwards at the near post by Pilkington, but Federici pushed it out for a corner.
Jim Gannon decided to bring on McSweeney on 63 minutes and less than 60 seconds he levelled after picking up the ball in the Southend half and unleashing a 25-yard right-foot shot into the top right corner of Federici's goal.
The Shrimpers were reduced to ten men on 68 minutes when Dan Harding got a harsh straight red card from referee Trevor Kettle following a late challenge on McSweeney.