The victory for Ronald Koeman’s men makes it four in a row in the Premier League and follows on from the midweek success at Arsenal which took Saints into the Capital One Cup fourth round.
All the goals at St Mary’s on Saturday came in the second half. On-loan Chelsea left-back Ryan Bertrand opened the scoring in the 54th minute with a fine finish after Sadio Mane’s backheel.
Rangers hit back through Charlie Austin’s excellent swivel and shot on 66 minutes, but just two minutes later, Pelle came up with an acrobatic winner after being set up by Dusan Tadic’s header.
The win keeps Saints in second spot, three points behind leaders Chelsea after six games, while QPR remain 18th in the table.
Both teams made two changes. Toby Alderweireld was back for Saints after a hamstring strain and Bertrand also returned to the defence, with teenager Matt Targett dropping to the bench and Florian Gardos missing out through injury.
Sandro was back from a knee injury for QPR, and Matty Phillips started on the right after being a first-half substitute a week ago in the 2-2 draw at home to Stoke. The man he replaced, Joey Barton, dropped out along with Jordon Mutch – both picked up hamstring injuries a week ago.
Visiting manager Harry Redknapp received the hate-filled welcome he anticipated, after quitting Saints for bitter rivals Portsmouth in 2005. The ex-Tottenham boss was subjected to vitriolic chanting from home supporters from the moment he emerged.
Tadic spent the first half gamely battling to cajole Southampton’s staccato attack into something resembling fluency.
Despite his best efforts however, the hosts were unable to break the deadlock before the break, even with QPR remaining largely toothless up front.
Morgan Schneiderlin squandered the chance of the half, screwing his low shot well wide after being sent clean through by Mane.
Serbia forward Tadic wasted a gilt-edged chance himself, unable to connect cleanly enough in the box to provide the power to beat Rob Green.
The relieved Rangers keeper tapped wide at full stretch when Tadic should have buried his point-blank effort.
None of Saints’ big men were able to meet Tadic’s early whipped free-kick with any accuracy early on and that missed opportunity set a frustrating tone for the opening exchanges.
Pelle fired wide of Green’s left post when he could have aimed across goal too, as Saints continued their wasteful half.
Eduardo Vargas and Austin spent precious little time combining with their midfield to offer any tangible threat for Rangers, but Niko Kranjcar and Leroy Fer had to shoulder their share of blame for not bridging the divide.
Phillips blasted high and wide after a botched clearance from Nathaniel Clyne, before Austin chipped wide in first-half stoppage time.
Redknapp’s men were fortunate to turn around on level terms, desperately hoping to grow in stature with every chance Saints fluffed.
Just when the visitors thought they could frustrate Southampton into a costly error though, Koeman’s men opened the scoring.
Mane’s prescient backheel opened the QPR defence, Bertrand raced through the door and blasted the ball under Green to wrestle control for Saints in the 54th minute.
Austin disabused any Saints notions of coasting to victory with a fine finish 12 minutes later, firing home on the spin after controlling Vargas’ cross.
Rangers’ return to level terms was meant to stun Saints into a state of shock, but instead the hosts struck straight back.
A peripheral figure for much of the afternoon, Pelle forced the game to turn on his acrobatic finish.
The Italian striker teed himself up before unleashing an unstoppable scissor-kick blast into the top corner to put Saints 2-1 to the good only two minutes after the visitors had levelled.
Steven Davis rattled the woodwork from 20 yards as Saints pressed again, before Austin headed wide in another fine opportunity for QPR.
Kranjcar hit the angle of post and bar for QPR as Redknapp’s men ground on in search of a second equaliser.
Tadic struck a post as the match edged into stoppage time, but Saints eased to victory despite failing to add a third goal.
They travel to face former coach Mauricio Pochettino’s Tottenham on Sunday week, a match that immediately precedes QPR’s next assignment at West Ham.