Smallbone gave Saints the lead just 90 seconds into the second-half after Shane Long saw his goal ruled out through VAR approaching the break.
Long was adjudicated to have been offside upon review by the slightest of margins but Smallbone wouldn’t be denied his goal as he thrashed in an effort from close-range.
Vokins then added a second when he thumped his shot off the underside of the bar to put Saints ahead 2-0 three minutes from full-time.
Southampton: Gunn, Vokins, Yoshida, Vestergaard, Danso (Cedric 75), Ward-Prowse Romeu, Smallbone (Armstrong 70), Boufal (Obafemi 78), Adams, Long
Unused subs: Lewis (GK), Stephens, Slattery, Ings
Goals: Smallbone (47), Vokins (87)
Bookings: Long (42)
Huddersfield: Coleman, Brown, Stankovic, Schindler, Simpson, Hogg, Chalobah, Hadergjonaj, O’Brien (Koroma 83), Bacuna (Grant 66), Campbell (Mounie 62)
Unused subs: Schofield (GK), High, Daly, Harratt
Referee: Tim Robinson