Southampton won for the second consecutive week to keep Huddersfield Town in the relegation zone after a fifth straight defeat.
Ralph Hasenhuttl's side were 2-0 up at the break thanks to Nathan Redmond's cool strike and a Danny Ings penalty.
The hosts improved after the break and halved the deficit through Philip Billing's swerving, long-range effort.
But 18-year-old substitute Michael Obafemi's first Premier League goal sealed the win for the Saints.