The Hoops’s preparation for the trip to St Mary’s was disrupted by reports that their warm-weather training camp in Dubai last month in fact turned into an alcohol-fuelled holiday.
But Redknapp rubbished the speculation on Saturday morning, and the west London side made a bright start as £8m striker Loic Remy edged the visitors ahead in the 14th minute.
The Saints drew level through Gastón Ramírez, with the midfielder lifting his finish over Hoops keeper Júlio César after the Brazilian failed to parry Jay Rodriguez’s shot to safety.
But QPR handed Redknapp the perfect 66th birthday present when Park Ji-Sung’s tenacious run teed up Jay Bothroyd, who finished from close range in the 77th minute to help the Hoops move to within four points of safety.
“We’ve let our football do the talking. The article in the paper was a total non-story. Write us off at your peril,” said Redknapp.
“Everyone put a shift in. We didn’t carry anyone today. It’s the perfect birthday present.”
He added: “It was a big result for us, it’s a difficult place to come and Southampton are a good team, but that’s what you get when you all work hard. I picked 11 players to work hard and when you work hard you get your rewards.
“Loic Remy looked sharp off the right and took his goal well. It’s just a case of getting him fit. Jay Bothroyd has not had many opportunities, I played him today and he did well.”
Despite beating Southampton, Redknapp believes that his former club, who are three points clear of the bottom three, will beat the drop this term.
“I don’t see Southampton getting sucked into a relegation battle. They are a good side, although you never know,” he added.