The Israeli champions went into the game knowing either a win or score draw would be enough to see them through into the last 32 of the competition.
The visiting support provided a noisy backdrop at St Mary’s, though could have been quietened in just the second minute, when from a corner, Charlie Austin, unmarked, headed straight at David Goresh in the Be’erSheva goal.
Fraser Forster was then called into action at the other end, when Mihaly Korhut got down the left-hand side, his cross from the touchline only gathered at the second attempt by the England goalkeeper.
It was Maor Buzaglo who had the first clear-cut chance of the game in the 18th minute when the ball fell to him 15 yards out, but he couldn’t keep his angled drive down as he blazed his effort over the bar.
Goresh was then called into action, diving full stretch to parry away Nathan Redmond’s curling effort, in what was the last notable action of the first half.
The second half was only five minutes old when Be’erSheva manufactured its first chance, but former Chelsea striker Ben Sahar saw his goal-bound shot from eight yards out brilliantly blocked by Maya Yoshida, before at the other hand, Shane Long had a similar effort, but saw his attempt deflected behind for a corner.
Southampton should have gone ahead in the 67th minute when Virgil Van Dijk failed to hit the target from a corner, with Goresh grasping at thin air.
Buzaglo’s moment of brilliance arrived in the 77th minute when he arrowed in a superb shot past Forster, after Yuval Shabtai had stole possession, meaning The Saints now needed two goals to go through and deny Be’erSheva progression to the last 32.
Pushing forward for those two goals, the Israelis looked dangerous on the counter-attack, and relatively comfortable in defence. That was until Van Dijk got a lucky break in the box and saw his shot from eight yards out deflected past Goresh.
Maya Yashida arguably should have scored their second, but headed inches wide, which would prove to be the last attempt of the game as Be’erSheva sealed a famous win.