Goals from Marcus Barnes, Jonathan Afolabi and Sam McQueen put the Saints in command at the break.
Newcastle cut the deficit to 3-2 thanks to Tom Heardman's header and Jamie Sterry but Southampton made the match safe through McQueen again, substitute Tyreke Johnson and a James Ward-Prowse free-kick.
The win puts Saints fifth, two places above Newcastle.
Southampton travel to Norwich City on Friday while Newcastle host Blackburn Rovers the same day.
(Photo courtesy of Matt Watson/Southampton FC)