Goals from Morgan Schneiderlin, Rickie Lambert, Jay Rodriguez and Sam Gallagher did the damage at St Mary's as Mauricio Pochettino's side moved eighth in the Barclays Premier League at the end of a week in which Ralph Krueger was appointed chairman.
Things are far less rosy at Norwich, with the 4-2 defeat a bad start to a vital few weeks that may well define their fate, given they face Liverpool, Manchester United, Chelsea and Arsenal in the final four fixtures.
City deserve credit for the way they reduced the deficit but that will do little to alleviate the pressure on Hughton, who was subjected to chants of "you don't know what you're doing" after making a triple second-half substitution.
By that point Norwich were behind to a fine early team goal by Schneiderlin and a Lambert effort just a minute after he replaced captain Adam Lallana.
The onwatching Roy Hodgson will been impressed by the forward's impact as he also provided the assist for Rodriguez, before City attempted a remarkable comeback.
Sloppy play allowed Johan Elmander and Robert Snodgrass to reduce the deficit and set up a tense finale, although 18-year-old Gallagher's first Premier League goal put the game out of sight and will raise fresh questions over Hughton's future.
The Norwich boss made five alterations to the side held to a 1-1 draw by Stoke last weekend, so it was perhaps no surprise that they began shakily.
Gaston Ramirez, making his first league start since New Year's Day, headed over inside the opening 90 seconds and then provided the opening goal with just five minutes on the clock.
Steven Davis, Rodriguez and Ramirez were all involved in the move, with the latter playing a wonderfully weighted ball through for Schneiderlin to turn past John Ruddy.
Davis glanced a header wide soon after the Frenchman's 10th goal for Saints, before Joseph Yobo used his strength and experience to stop Rodriguez getting a shot away after latching onto a fine Lallana pass.
James Ward-Prowse did well to stop Gary Hooper capitalising on defensive confusion in a rare moment of respite for Norwich, who soon saw Davis and Ramirez come close from the edge of the box.
Referee Kevin Friend waved away appeals from Norwich's players for handball against Jose Fonte on the edge of the Saints box. Eight City players surrounded the referee in the next break of play, which was soon followed by Hooper wasting Norwich's best chance of the half by firing into the side-netting.
Davis was booked for a strong challenge on Martin Olsson as frustrations began to come to the surface, with the Norwich full-back involving in a tussle with Rodriguez soon after.
Anthony Pilkington was booked for attempting to turn in a Hooper cross with his arm and Southampton fans became audibly frustrated with Artur Boruc's poor kicking as half-time approached.
The Poland goalkeeper continued to look shaky when play resumed, although Saints were back in the ascendancy.
Ward-Prowse forced Ruddy into action with a 25-yard strike, before the teenager sent in a corner which Rodriguez nodded just wide.
In an attempt to put the match to bed, Pochettino surprisingly withdrew captain Lallana after 57 minutes - but it reaped immediate rewards.
Fonte's long ball was flicked on as Ramirez put pressure on the Norwich defence, with the ball falling kindly for Lambert, who turned past Yobo and slotted impressively past Ruddy.
The goal saw Hughton take drastic action, bringing on Elmander, Nathan Redmond and Ricky van Wolfswinkel in the 65th minute.
However, Saints soon pulled further ahead. Ruddy did wonderfully to deny substitute Guly do Prado, but the rebound fell for Lambert to flick onto Rodriguez to net.
The England forward rattled the crossbar with an incredible long-range effort and Ruddy denied Lambert as Saints looked to pull further ahead, before Norwich launched an improbable comeback.
With 85 minutes on the clock, a wayward Fonte backpass fell kindly for Elmander and the on-loan striker slotted coolly past Boruc.
A minute later and more sloppy Saints play saw Norwich further reduce the deficit.
This time Guly was the guilty party, losing possession as Van Wolfswinkel tested Boruc and Snodgrass struck home the rebound.
It was an ending few could have predicted and, having held on following an injury to Dejan Lovren, Saints broke to put the game out of sight. A slip from Yobo saw Davis race through and square for teenager Gallagher, whose shot crossed the line before it was hacked away.