Grzegorz Rasiak scored twice on the day QPR mourned the tragic loss of teenage striker Ray Jones.
Rangers paraded Renault Formula One chief Flavio Briatore, who is buying the club along with Bernie Ecclestone.
But the mood around Loftus Road was sombre as wreaths were laid and a minute's applause was held in honour of Jones, who was killed in a car accident last weekend.
Clearly affected by their traumatic week, the home side played poorly.
They started reasonably well though and had appeals for a 14th minute penalty ignored by referee Mike Thorpe.Dexter Blackstock latched onto a pass from Mikele Leigertwood and went down under a challenge from Southampton's Wayne Thomas, whose tackle was deemed to be a fair one.
Thomas was at the centre of the action again two minutes later when his shot was tipped over by keeper Lee Camp .
But Camp was beaten when the resulting corner by Youssef Safri was headed home by Rasiak.
Rangers again appealed in vain for a penalty when Jermaine Wright appeared to pull back Martin Rowlands.
First the striker shot straight at Camp after being put through by Damion Stewart's woeful back pass.
Then, shortly afterwards, he lost his footing at the crucial moment after being found unmarked by Nathan Dyer.
But Rasiak did get his second goal just before the break.Jhon Viafara went rampaging through the Rangers defence and was sent sprawling by Camp. The loose ball fell to Rasiak who had the simple task of slotting into an empty net.
Five minutes into the second half, Dyer had produced a great deal of skill on the right and crossed for Bradley Wright-Phillips to head in Southampton's third.
Another error by Stewart handed Rasiak his chance to complete his hat-trick, but the Pole's lob over Camp was weakly struck and Stewart recovered to clear the ball off the line.
Rasiak then missed two good chances to put the Saints further ahead.