Barr struck in the 70th minute to win what was a tight contest played out in tough conditions, leaving Gary Bollan’s men on the tails of Dundee and Partick Thistle in third and fourth place respectively.
Strong winds meant football became an increasingly difficult art to master, and both teams struggled to put together much in the way of good play in the opening 45 minutes.
Alan Combe in the home goal was alert to tip a deflection of his own defender round the post, and also denied Liam Fox with a smart save to his right. Kenny Deuchar headed the rebound home but he was flagged offside.
A fine Keaghan Jacobs through ball then played in Bobby Barr, but the winger skewed his effort wide.
Hamilton’s Dougie Imrie and ex-Lion Gordon Smith caused problems in the visitors’ box, but Livi scrambled clear after Andy McNeil had beaten away an angled drive.
Accies started as the stronger side in the second period, whipping dangerous balls into the box, but McNeil in the away goal held firm to keep Billy Reid’s men at bay.
As the game moved past the hour park Bollan brought on striker Mark McNulty for injured left back Jason Talbot, and the Lions turned the screw on their hosts. Keaghan Jacobs robbed Accies of the ball before skipping past two defenders, but his low shot was parried by Combe.
Mark Fotheringham was soon to follow the effort up, but his strike sailed wide of the left hand post. Gary Fraser responded for Accies, his own effort from the corner of the box whistling just over McNeil’s bar.
With twenty minutes remaining the Lions broke the deadlock in spectacular fashion. Bobby Barr picked the ball up on the left hand side before cutting across the edge of the penalty area and unleashing a vicious drive that bulleted past Combe into the top corner.
The goal saw the home side desperately scramble for an equaliser, but despite the bulk of the possession in the closing stages, they struggled to create a clear opportunity at goal.
Smith headed over from five yards when he was set up with a golden chance to draw Billy Reid’s men level, and Livi held out for all three points.