Jose Fonte's second half strike saw Southampton extend their unbeaten run to six Barclays Premier League matches at Hull, who remain within touching distance of the relegation scrap.
Saints were good value for three points, maintaining a fierce tempo throughout at the KC Stadium and creating a host of fine chances.
Rickie Lambert and Jay Rodriguez were both in profligate mood, raising Hull's hopes of a battling draw, but Fonte settled things in the 69th minute when he stabbed over the line.
The Portuguese defender needed the Goal Decision System to claim the goal, with Lambert rifling home on the follow-up.
Lambert had earlier missed a pair of wonderful chances in the opening seven minutes, while Rodriguez struck the crossbar.
Hull were far from passengers in the contest, striking the woodwork first when Shane Long's header kissed the inside of the post, but they could not match Saints' energy around the park and tired visibly.
Having taken four points from Tottenham and Sunderland this month, their attempts to pull clear of the strugglers were duly stalled.
Adam Lallana wasted no time in carving out an early chance for Saints, clipping in a cross.
Curtis Davies deflected into the ball into Lambert's path and he looked certain to score, only to shoot a yard wide from 12 yards.
Things continued at a lively pace and on the half-hour mark, Southampton again came close.
Hull failed to close down Rodriguez 20 yards from goal and he proceeded to lift a delicate shot flush against the crossbar.
Hull were firmly on the back foot after the restart. But for all their superiority, Southampton were struggling to find a finish.
Hull were quickly settling into a siege mentality, though the decision to leave both Jelavic and Long up front meant the visitors could not afford to switch off.
The home side's defence eventually buckled on 69 minutes.
Harper played his part, getting down to keep out Fonte's headed effort and then recovering to make a point-blank block from Lallana.
The ball squirmed loose and returned to Fonte, whose side-footed effort crept over the line.
Goalline technology confirmed the ball had crossed but it would not have affected the scoreline, with Lambert following up.
Either side might have scored in a frenetic closing period, but somehow the ball stayed out and Southampton collected the win.