The Shrimpers extended their unbeaten run to 13 games as Carlisle’s promotion hopes received a setback.
Southend were rewarded when Paul Reid fouled Barnard and Charlie Mulgrew netted the subsequent free-kick.
Gary Madine won a free-kick and Simon Hackney’s delivery deceived keeper Darryl Flahavan as Carlisle equalised.
Home defender David Raven was red-carded in the 67th minute for a late challenge on Nicky Bailey. Carlisle still should have led a couple of minutes later but Graham headed over.
Barnard came close for the visitors in the 86th minute when his curler hit the inside of the far post. But in the 90th minute Gower’s cross gave the Southend striker the chance to thump home a header.