The points are shared at Maiden Castle as Durham put another big point on the board.
Durham started the game well, with a handful of big chances from Mollie Lambert within the opening minutes.
Another early chance came in the 9th minute from Dee Bradley as she nodded the ball just wide from close range following a scramble in the box.
Southampton skipper Atlanta Primus managed to pick the back of the net out in the 27th minute, but the goal was ruled offside.
Making a handful of changes in the second half, Durham continued to be the stronger side.
In the 88th minute, breaking in behind the Southampton defence, Lambert played a low cross in behind to Grace Collinson, but the ball was snatched away from her at the last second by the Southampton defender.
Lucy Watson almost won it for Durham in the 93rd minute through a free kick, but her effort was pushed acrobatically over the bar by Stenson, as it headed for the top right corner.
Durham continued to push hard to find the winner, but were unable to find a breakthrough.