Che Adams and Stuart Armstrong scored either side of the break for Saints, who were without Ryan Betrand and top scorer Danny Ings.
Ings is set to miss the next four to six weeks with a knee injury that he picked up last Sunday against Aston Villa.
Southampton started bright and grabbed the lead on eight minutes when Adams turned in Theo Walcott’s cross on the volley to beat Karl Darlow for pace.
Newcastle mustered little attack throughout the game and their lone chance on target came when Sean Longstaff headed directly into the grasp of Alex McCarthy on 22 minutes.
Walcott nearly turned goal scorer just before halftime when he latched onto Moussa Djenepo’s smart-flick on, but the forward who started in place on Ings curled his effort wide of the post.
Saints maintained their momentum to start the second half and came close to doubling their advantage through Jan Bednarek only for the defender to see his header cleared off the line by Jamaal Lascelles.
Oriol Romeu then had Darlow push his attempt from distance off the crossbar, before Bedarek was denied from point-blank with Saints looking to find their goal to hold off Newcastle.
Armstrong prevented a nervous finish for Saints when he made it 2-0 with a left-footed shot that found the bottom corner seven minutes from full-time.
Joelinton tried to pull one back late, but McCarthy was equal to the task as he made an outstanding save to preserve Southampton’s two-goal lead, which was enough to see them leap over Liverpool at the top of the Premier League.
Southampton (4-4-2): McCarthy; Stephens, Vestergaard, Bednarek, Walker-Peters; Djenepo (Redmond 73), Romeu, Ward-Prowse, Armstrong; Walcott (Long 88), Adams
Unused subs: Forster (GK), Ramsay, Diallo, Tella, Long, N’Lundulu
Goals: Adams (8), Armstrong (82)
Bookings: Romeu (27)
Newcastle United ` (5-3-2): Darlow; Lewis, Fernandez, Lascelles, Schar, Murphy (Joelinton 79); Almiron, Hendrick (M. Longstaff), S. Longstaff; Saint-Maximin, Wilson (Carroll 78)
Unused subs: Gillespie (GK), Hayden, Manquillo, Clark
Bookings: Fernandez (43), S. Longstaff (90)