The first half was goalless before the match exploded into life after the interval, with Muhammed Demirci breaking the deadlock for the Turkish club with a spectacular long-range strike into the top corner.
Stung into action, Saints drew level as Rickie Lambert controlled a Jack Cork free-kick with his chest and was given time to bring the ball down and drive his shot home.
Emmanuel Mayuka put Southampton ahead with a dipping left-foot volley from the edge of the box which beat the keeper at his near post.
Lloyd Isgrove then sealed an impressive win just before the final whistle as he supplied the finishing touch to a Luke Shaw pass from six yards.
Southampton will now head home for a few days before taking on Celta Vigo in Spain next weekend.