The visitors performed admirably on the south coast and opened the scoring after just 14 minutes through Loic Remy.
Saints looked shell-shocked having started the brighter and were somewhat fortunate to go in at the break level, with Gaston Ramirez following up a Julio Cesar fumble.
Southampton manager Mauricio Pochettino - coincidentally also celebrating his birthday - sent his side out with renewed vigour but again they were caught napping.
Park Ji-sung sent a low cross from the right and Jay Bothroyd slotted home to the delight of Redknapp, abused throughout by the home supporters.
Substitute Robert Green, on for the injured Cesar, did superbly to deny a late Maya Yoshida header but, despite a late onslaught, QPR held on for victory.
Saints had the better start and it took just 13 seconds for Adam Lallana to send over a cross which Christopher Samba was forced to put out for a corner.
QPR went ahead when Junior Hoilett, making his first start since January 2, sent a fine through ball over to Remy, who burst through on goal to strike past Artur Boruc. Danny Fox got the final touch as he attempted to hook the ball clear, although it was the Frenchman that deservedly took the credit.
Saints drew level through Ramirez, who dinked home nonchalantly after Jay Rodriguez struck an audacious effort that inexplicably bounced off Cesar.
Fox, Jose Fonte and Rickie Lambert all had attempts before Rodriguez's curling effort from the edge of the box went inches over. Saints were again caught napping with 13 minutes remaining. After excellent work down the right, Park sent over a low cross for Bothroyd to rifle home.