On-loan defender Ryan Bertrand opened his Saints account to hand the hosts the lead before Charlie Austin blasted home on the turn.
Italian striker Pelle trumped Austin's smart finish with a true showman's goal to secure Saints' fourth win in six Premier League ties this term.
Former Southampton boss 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, but would have chuckled to himself when Austin stole the second half equaliser.
The former bricklayer had a fine chance to double his tally, but headed wide, while Nico Kranjcar also hit the woodwork with a fine free-kick.
The ex-Portsmouth midfielder fired a set-piece goal to steal QPR a point against Stoke last weekend, but was just unable to repeat the feat at St Mary's.
Pelle's stunning volley won the day however, the £8million summer recruit notching his fifth Southampton goal.
Southampton's victory kept them second in the table, after Chelsea eased past Aston Villa at Stamford Bridge, to continue new boss Ronald Koeman's fine Premier League start.
Dusan 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 Sadio Mane.
Serbia striker 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 Kranjcar and Leroy Fer had to shoulder their share of blame for not bridging the divide.
Matt 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 back heel 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 tie 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.
Source : PA
Source: PA