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Following a low-key start, Eljero Elia had the first shot of the night on five minutes, but his effort soared high above the bar.
Midway through the first half, a penalty appeal for Palace was waved away as Dwight Gayle tumbled under a challenge in the box.
Just after the half-hour mark, the Eagles nearly broke the deadlock when Fraser Forster dropped a Yannick Bolasie cross with Wilfried Zaha set to capitalise, but the Saints stopper did enough to get back and keep the ball out.
Southampton ended the first 45 minutes on a high as Elia burst in late on and fired in a low shot towards goal, but Julian Speroni got down well to make the save.