Victory was the ideal tonic for Redknapp after waking up on his 66th birthday to damning reports of ill-discipline on a recent Dubai training camp.
Rather than throw the strugglers off track, though, QPR 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 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.
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, whose side were on the backfoot from the outset.
It took just 13 seconds for Adam Lallana, making his first home start in almost three months, to send over a cross which Christopher Samba was forced to put out for a corner.
Jack Cork and Lallana put audacious long efforts wide as Saints continued to press for an opener, which almost came after 12 minutes.
Rickie Lambert, always dangerous at the back post, headed back across goal but neither Lallana nor former QPR winger Jason Puncheon were able to get a telling touch.
Referee Howard Webb waved away penalty appeals from the pair, and after Lallana volleyed wide, the west Londoners caught Southampton off guard.
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 in front of the 3,194 visiting fans.
Danny Fox got the final touch as he attempted to hook the ball clear, although it was the Frenchman that deservedly took the credit.
Southampton looked visibly shell-shocked by the goal and Nathaniel Clyne did well to deny Remy going through again, before the returning striker tested Boruc with a low strike.
Bothroyd and Stephane Mbia were both booked as QPR continued in the ascendancy, before Lallana crashed into Clint Hill as he looked to break through.
After a lengthy break in play for treatment, Lallana, looking decidedly groggy, was replaced by Jay Rodriguez in the 43rd minute.
While QPR were still threatening, Saints had a new spark and, after seeing a shot deflect behind, Ramirez drew parity.
Rodriguez struck an audacious effort that inexplicably bounced off Cesar into the path of Ramirez to dink home nonchalantly.
Armand Traore and Jose Fonte were booked either side of the goal for poor challenges, but there was no doubt about Morgan Schneiderlin joining them in Webb's notebook in stoppage time.
Mbia looked set to score from close range before the Frenchman's exquisite sliding tackle, with Bothroyd firing the loose ball wide.
The half-time whistle will have come as a relief for a Southampton side fortunate to be level.
Whatever Pochettino said at the break seemed to work as the home side flew out the blocks.
Fox, Fonte and Lambert all had attempts, before Rodriguez's curling effort from the edge of the box went inches over.
Luke Shaw came on for Fox in the 57th minute after the left-back appeared to pick up a knock as Saints continued to build nicely.
Cesar was hurt in a collision with Rodriguez as he punched away a threatening Cork cross but hobbled on, only to spill another long-range Rodriguez strike moments later.
Green soon replaced the injured Brazilian, but not until after Hoilett threatened at the other end.
Saints were still on top but they were again caught napping. After excellent work down the right, Park sent over a low cross for Bothroyd to rifle home with 13 minutes remaining.
Southampton rallied and peppered the QPR goal in the closing stages.
Green did fantastically to deny a goalbound Yoshida header as the hosts upped the ante but they could not find a way past the Hoops' resilient backline.