Southampton took the lead from the first chance of the night. An inswinging corner from Dan Fox found Hooiveld and his downward header beat Paul Jones.
Nigel Adkins' side doubled their lead five minutes later when Adam Lallana burst into the area and could have gone down under challenge. He stayed on his feet and managed to dig out a cross to Richard Chaplow who nudged the ball to Sharp and he slammed home.
Posh started the second half on top, with Shaun Brisley heading into the arms of Davis and Barnett nodding past the left hand post from George Boyd's centre.
But Southampton stepped it up and added a simple third in the 57th minute when Rickie Lambert's cross-shot found its way to Sharp and he slid in his second of the night and sixth goal in as many games.
Tommy Rowe should have done better with a shot from inside the area in the 85th minute, and after Taylor had stung the palms of Davis again, Rowe did manage to pull a goal back. A low cross from Barnett was coolly converted by Rowe from six yards.