Saints coach Ralph Hasenhuttl rested his first-team stars, with the likes of Alex McCarthy, Cedric Soares, Jack Stephens, Nathan Redmond and Danny Ings all sitting out the contest.
Despite the changes, Southampton made a fast start, with Smallbone and Shane Long forming a solid partnership in the final third.
The young midfielder had the first chance of the match, but his shot from inside the box sailed over the crossbar.
Huddersfield responded but Fraizer Campbell produced a similar effort and found the back of the stand at St Mary’s after a good ball from Lewis O’Brien.
The hosts thought they had scored on the stroke of half-time, but Long’s goal was ruled out for offside after the officials consulted VAR.
Replays suggested the decision was harsh as both teams failed to make their mark before the break. It did not take Southampton long to score in the second half though, with Hasenhuttl’s side 1-0 up inside the 47th minute.
Kevin Danso’s cross from the right-wing was met by Long who cushioned his header into the path for Smallbone to volley home.
Huddersfield failed to offer much in reply on the south coast, and the gulf in class between the sides was clear to see for the majority of the 90 minutes.
Southampton still needed a second goal to make sure of their place in the fourth round and eventually sealed the win with three minutes to go. Che Adams’ pass found Vokins on the edge of the Huddersfield box, and the winger smashed the ball home off the underside of the crossbar.
Hasenhuttl can now look forward to the fourth-round draw, while Huddersfield’s attention turns back to the Championship and their fight for survival.