Jay Bothroyd's strike 13 minutes from time saw the Hoops take all three points in a crunch encounter at St Mary's.
The 48-year-old businessman, who took control at Loftus Road in August 2011, revealed his delight on Twitter, while also wishing manager Harry Redknapp a happy birthday.
He posted: "Proud of my players and my manager. Happy birthday Harry."
The result sees Rangers draw within four points of safety.