The hosts comfortably defeated the Tigers after two goals, one from the Italian and a penalty from youngster James Ward Prowse, to maintain their European hopesHull City defender Alex Bruce was left to rue a clumsy challenge after conceding the penalty that sent Southampton on their way to a 2-0 Premier League victory on Saturday.
Relegation-threatened Hull had shown signs of picking up a much-needed result in the first half, with Sone Aluko proving a constant nuisance to the Southampton back line.
However, Bruce lunged in on former Hull striker Shane Long to concede a 56th-minute spot-kick, and James Ward-Prowse – previously without a league goal to his name – made no mistake in finding the net.
James Chester came agonisingly close to restoring parity soon after when he saw a header cleared off the line by Ryan Bertrand, but Graziano Pelle made sure of maximum points with his first Southampton goal of 2015 nine minutes from time.
The result leaves Hull two points clear of the drop zone with just six matches left to play, including clashes with Liverpool, Arsenal, Tottenham and Manchester United.
Wins for Burnley or QPR, who face Arsenal and Chelsea respectively this weekend, would see Hull slip into the bottom three.
Goalkeeper Allan McGregor was dropped to the bench following a disappointing performance in a 3-1 defeat at Swansea City last weekend and replacement Steve Harper – one of five changes for the visitors – soon came under pressure from Long, who was unable to make the most of a loose Jake Livermore backpass.
An open start to proceedings saw Aluko poke just wide at the other end moments later, before the striker tested Kelvin Davis with a low drive.
Harper went some way to justifying his selection by making himself big to keep out Pelle from close range after 20 minutes, while Aluko continued to give the home defence plenty to think about.
The Nigeria international's next effort swerved just wide from 25 yards, and Morgan Schneiderlin was lucky to escape a booking for a frustrated lunge on the Hull forward on the half-hour mark.
An advancing Aluko was then tugged back by Victor Wanyama, who was shown the yellow card and will miss Southampton's next two matches as a result.
Davis got down well to his left when Livermore - teed up by Aluko - fired a low drive at the bottom corner early in the second half, but a clumsy Bruce challenge on Long in the box proved costly.
Ward-Prowse coolly slotted home from the resulting penalty, but Chester would have restored parity soon after had his header not found a well-placed Bertrand on the line.
Any hopes of a turnaround were dashed after 81 minutes, when Pelle - who had not scored since December - tucked in a low strike from a Schneiderlin cutback.