Anthony Pilkington netted his fourth goal in three games by thrashing a 25-yarder into the top-right corner after six minutes, after the Saints defence failed to clear a Graham Carey corner.
More slack defending at a set-piece in first-half stoppage time was punished by another 25-yard strike, this time by Joey Gudjonsson after Jose Fonte's weak headed clearance.
Southampton keeper Kelvin Davis kept the score down by tipping a Carey free-kick against the bar early on and he then beat away another Gudjonsson drive after 33 minutes.
Southampton, who had not conceded a goal since Adkins took charge last month, nearly got back into it when Adam Lallana crossed for Rickie Lambert after 36 minutes. But Lambert's powerful header was cleared off the line by Damien Johnson.
Saints were also denied early in the second half by Lee Peltier's saving tackle on Guly Do Prado.
Terriers keeper Ian Bennett also saved well from Lambert after 57 minutes before the game was delayed by an injury to a linesman.
That led to 11 minutes of stoppage time being added on and Southampton kept pressing but failed to stage a comeback.