Both sides came close to breaking the deadlock with clear-cut chances in the first period, but ultimately cancelled each other out during a hard-fought encounter.
The Saints showed attacking ambitions from the off and almost took an early lead when Charlie Austin gained possession in the box and beat Kasper Schmeichel from an acute angle, only to be denied by the post.
Dangerous as ever on the counter-attack, Leicester looked odds-on to break the deadlock in the 30th minute when Jamie Vardy latched on to a bad backpass by Virgil van Dijk and rounded Fraser Forster in the Saints goal, but Oriol Romeu produced an instinctive block on the line before denying Islam Slimani on the follow-up.
Goalscoring opportunities proved fewer in the second half, but Southampton came close just after the hour mark when the in-form Austin raced clean through on goal and attempted to lob Schmeichel, but the Foxes stopper anticipated the chip and stood tall to make the save.
Moments later, Claudio Ranieri's side were back on the front foot as Danny Drinkwater powered his way through the Saints defence, shrugged off a challenge from Romeu and rifled a shot into the side-netting.