Southampton took the lead in the seventh minute when Steven Davis pounced after a brilliant free-kick from James Ward-Prowse came back off the woodwork.
But Saints were unable to build on their bright start and there was little in the way of goalmouth action for the remainder the half.
Newly promoted Brighton levelled shortly after the break when Glenn Murray headed in a Pascal Gross cross from the right at the back post.
Goalkeeper Fraser Forster got a hand to the ball but could not prevent it finding the top corner.
As the half wore on there were chances for each sides and both managers made changes in an effort to force the decisive breakthrough but they had to settle for a draw.
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