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
More than 30 huts have been burgled along Herne Bay pier, in what seems to be a systematic attack
More than 1,000 cars have been left unattended in a muddy field by companies promising to provide 'off-site' parking for Gatwick Airport.
More than 1,000 cars have been left unattended in a muddy field by five companies promising off-site parking for Gatwick Airport.