Saints looked shell-shocked having started the brighter and were fortunate to go in at the break level, with Gaston Ramirez following up a Julio Cesar fumble.
Saints manager Mauricio Pochettino also celebrating his birthday sent his side out with renewed vigour but they were caught napping.
Nearly all the pre-match build-up surrounded Redknapp's first return to Southampton, who were relegated eight years ago under his leadership before he then rejoined bitter rivals Portsmouth.
"You're going down with the Redknapp" was one of the few polite chants directed at the QPR boss.
More top news
Very windy with heavy rain moving east tonight. Becoming drier but staying windy later. Then sunny spells and strong winds tomorrow
Heavy rain and strong winds this evening. The rain will clear tonight but staying windy, especially along the coast
Hampshire police arrest seven more men in investigation into an alleged conspiracy to commit serious sexual offences on the Isle of Wight.