The visitors went ahead against the run of play in the first half with the Saints responding late in the same period, before Redknapp's men secured a vital win late in the day
Loic Remy's opener silenced the home supporters that were clearly fired up by the unpopular Redknapp's return, but Gaston Ramirez put the hosts level right before halftime.
And the crowd was stunned once more with just over 10 minutes remaining when Jay Bothroyd finished from close range to give the visitors all three points.
Despite a bright start by Saints it was the visitors who took the lead early in the game, Remy beating Artur Boruc in a one-on-one after some poor defending by the hosts allowed a long ball to fall to the Frenchman.
Mauricio Pochettino's side looked rocked by the goal as its earlier sharpness faltered a little, with a number of sloppy passes creeping into its play and attacking players failing to find the right final ball.
The sides failed to create anything of note for the majority of the rest of the half, with both sets of players' final ball still lacking. However, after coming on for the injured Adam Lallana, Jay Rodriguez's hopeful long-range effort was spilled by Julio Cesar, and Ramirez was on hand to chip delicately home to level the scores.
Shortly after the break Southampton center back Jose Fonte fizzed an effort just wide of the post, with the bright substitute Rodriguez also going close to adding a second.
The Saints continued to look the more dangerous side without really creating many chances, with Rodriguez going closest with another long-range effort spilled by Cesar.
However, again against the run of play, it was QPR which got the crucial next goal. Park Ji-Sung was allowed to stroll down the right wing before his low ball into the Saints area found an unmarked Bothroyd, who finished with ease.
Robert Green came on to replace the injured Cesar in the QPR goal, and the substitute was called into action late on producing a stunning save to deny Fonte's header by clawing the effort wide, and the Rs held on to end their winless run of six matches.