The result leaves the Cumbrians with just one win in six, but their hopes of automatic promotion still lay in their own hands and six points from their last two games will secure Championship football for next season.
The visitors made Carlisle pay for a terrible first-half display when Charlie Mulgrew's seventh minute 40-yard free-kick drifted over a clutch of defenders and crept inside Keiren Westwood's far post. Eleven minutes later Danny Graham finished neatly from Marc Bridge-Wilkinson's cross only to be hauled back for a dubious offside.
Barnard and Mark Gower both forced Westwood into good saves as the first half drew to a close but the Shrimpers never looked likely to land a second goal. A double substitution at half-time for Carlisle gave them some much-needed momentum before another fortunate free-kick gave the home side an equaliser.
Simon Hackney's curling cross from near the corner flag looked easy for Darryl Flahavan to gather but instead the keeper appeared to bump into his post and carry the ball over the line. Carlisle were now rampant with Hackney, Scott Dobie and Danny Livesey all going close but the home side's dominance was halted 23 minutes from time.
Referee Tony Taylor produced a straight red card for Raven for a foul on Nicky Bailey, who was himself very lucky to still be on the pitch after a series of bad challenges. With seven minutes remaining Barnard curled a delightful shot past Westwood only to see his effort strike the inside of the post and roll agonisingly along the line and out.
But the in-form striker wasn't to be denied and, deep into stoppage time, he headed home from six yards from Gower's perfect far post cross to send the visiting fans wild with delight.