The Shrimpers had gone four league games without a win before Barnard secured the points after 29 minutes.
Southend dominated the opening exchanges, with Kevin Betsy particularly dangerous down the right flank.
Dougie Freedman, making his home debut, was the first to test Hereford goalkeeper Darren Randolph with a shot the stopper parried for a corner.
Dean Beckwith then deflected a Lee Barnard shot out for a corner as the Shrimpers bypassed the Bulls' five-man midfield with ease.
The visitors clawed their way back into the match with Stephen O'Leary and Bradley Hudson-Odoi firing wide.
James Walker then shot straight at Randolph before the Bulls keeper was beaten in the 29th minute. Simon Francis' cross was deflected to Freedman whose pass allowed Barnard to score with a 12-yard shot.
Hudson-Odoi should have equalised from five yards out three minutes later but somehow shot wide.
Bulls midfielder Toumani Diagouraga then shot straight at Steve Mildenhall before Barnard's tame shot was saved by Randolph as the half finished.
The second period was played at a pedestrian pace until O'Leary tried his luck with a 25-yard shot which was parried by Mildenhall on the hour mark.
Mildenhall then received treatment for a knee injury after he had blocked a driven shot by substitute Matt Done.
With no keeper on the bench it looked like striker Alex Revell would go between the sticks, but a hobbling Mildenhall continued in goal.
And he denied Done in the dying seconds of the match after six minutes of stoppage time to ensure the Shrimpers secured their first league victory since beating Peterborough United 1-0 on the opening day of the season.