With managers in both dug-outs under severe pressure, first-half goals from Rickie Lambert and Jason Puncheon gave the Saints a deserved 2-0 lead at the break, before Junior Hoilett headed QPR back into the game early in the second period.
Southampton, though, kept pushing forward and secured the points seven minutes from time, when Adam Lallana's low cross was poked into his own net by Anton Ferdinand.
With the victory, Nigel Adkins' side have established a four-point gap between themselves and their beaten hosts.
Both he and Hughes stuck with the same starting line-ups that played last weekend, with Southampton the quickest to settle. Captain Lallana came close in the seventh minute, firing just over after a neat one-two with Gaston Ramirez, but their defensive frailties remained.
Adel Taarabt - so often a threat for QPR - drove in-between Nathaniel Clyne and Jose Fonte, before forcing a reaction save out of Paulo Gazzaniga, who then shovelled a Hoilett shot around the post less than a minute later.
Saints returned to the attack and got the game's crucial opener in the 23rd minute, when a corner was not cleared properly by the home defence. Ramirez pulled back for Fonte, whose shot was prodded goalwards by Puncheon. That effort was cleared off the line but Lambert showed his strength to bundle home.
Southampton pushed for another, which came on the stroke of half-time, when Puncheon collected the ball from Clyne, turned Alejandro Faurlin, and fired home a left-footed strike.
QPR were booed off at half-time after their inept display and Hughes replaced Faurlin with Jamie Mackie at the start of the second period, which was only four minutes old when Taarabt's floated cross was nodded home by the unmarked Hoilett.
Saints quickly retained their momentum, though, and Puncheon forced Julio Cesar into a smart save before firing wide twice within a minute.
The game was flowing from end to end and Cesar had to be at his best to deny a Maya Yoshida scissor-kick 10 minutes from time.
Nelsen headed straight at Gazzaniga moments later and then Saints secured victory, with Puncheon playing a short corner to Schneiderlin for the Frenchman's cross to squeeze in off Ferdinand at Cesar's near post.
QPR fans bellowed 'You're only here for the money' at their players and duly booed the side off at the end of the game, while Adkins and the Saints fans celebrated their first points earned away from home.