STEVEN Caldwell headed in his second goal of the season to give Burnley the lead in first-half stoppage time.
Southampton goalkeeper Richard Wright had only been called into action for the first time seconds early, as he stretched to tip over a Chris McCann header from Robbie Blake's free kick.
Blake took the resultant set piece, and captain Caldwell met it, unchallenged, to nod home.
Jensen had only just made his first save moments earlier, as he parried Andrew Surman's shot from distance.
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