Miguel Almiron continued his scoring streak as Newcastle consolidated their spot in the Premier League’s top four with another confident victory.
The Paraguay forward put the visitors ahead at half-time following a strong run and composed finish for his seventh goal in seven games.
Southampton, who are struggling for goals, wasted chances before Newcastle substitute Chris Wood swivelled sharply and fired into the corner.
The hosts were further punished when Joe Willock added the third, finishing a quick counter attack led by Kieran Trippier with an accurate finish.
From that point, Newcastle looked certain to extend their unbeaten run to nine matches.
Southampton did pull a consolation back through Romain Perraud’s fine solo strike, only for Bruno Guimaraes to restore the three-goal advantage with a superb curler.
The Saints have only won one of their past eight matches and will finish the weekend third from bottom.