Ryan Bertrand had given the hosts the lead before Charlie Austin's equaliser but it was the Italian forward who proved the match winner with a stunning overhead-kick
Pelle, a summer signing from Feyenoord, found the net with a stunning overhead-kick to secure a sixth successive win in all competitions for Koeman.
Ryan Bertrand had opened the scoring for the hosts early in the second half with his first goal for Southampton, which also served as his maiden strike in the Premier League.
|By Liam Twomey
Southampton approached this match on the crest of a pretty big wave, having made their best start to a top-flight campaign for 26 years despite a turbulent summer which saw much of the spine of the team replaced. They continue to surprise and deserved three more points against a QPR side who only decided to attack this match at 1-0 down and paid the price.
That St Mary's also witnessed two of the goals of the season - Charlie Austin's Bergkamp-esque control, swivel and volley, swiftly followed by a spectacular overhead-kick winner from Graziano Pelle - was merely an added bonus. Life is good on this part of the south coast right now and if things continue in their current vein, Southampton are far more likely to be dreaming of Europe than sweating over relegation in the final months of the season.
QPR, by contrast, are in a dire situation. For all their summer investment, this was their fourth consecutive away defeat in all competitions and a performance that only served to reiterate Harry Redknapp's apparent inability to mould this talented - if disjointed - group of players into a coherent and effective team. That they shackled Southampton for so long was a surprise, that they eventually buckled was not.
But Redknapp's hopes were dashed by the brilliance of Pelle, whose goal-of-the-season contender keeps Southampton in second place in the table.
It did not take long for the Saints to threaten the QPR defence as Robert Green was forced to deny Dusan Tadic after just five minutes, and the visitors' task was made even harder when midfielder Sandro was forced off with a head injury following an aerial challenge with Sadio Mane.
Sandro had recovered from a knee problem suffered in training this week in order to play at St Mary's Stadium but lasted just 11 minutes as he was replaced by Karl Henry.
Southampton's dominance was apparent throughout the first half, but the hosts were profligate in front of goal. Tadic was unfortunate not to open the scoring in the 19th minute, his low shot deflected against the post by QPR defender Steven Caulker.
Pelle should perhaps have done better a minute later as he failed to convert after being played through by Premier League debutant Mane, firing into the side netting.
Mane, who made his Southampton bow in Tuesday's League Cup win over Arsenal, was involved again as Morgan Schneiderlin went close to opening the scoring, the Frenchman shooting narrowly wide from close range as QPR's defence continued to show signs of weakness.
The pattern of the game remained unchanged in the second half and Southampton finally capitalised on their superiority in the 54th minute, although they were giving a helping hand from Green.
The former West Ham and Norwich City shot-stopper allowed Bertrand's effort to sneak under his body after the left-back had been put through on goal with a clever back-heel pass from Mane.
Green then somewhat atoned for that mistake by turning a Tadic chip over the crossbar from point-blank range.
QPR offered little in the way of attacking threat for the majority of the contest but found a perhaps undeserved equaliser in superb fashion after 66 minutes, Austin brilliantly controlling a cross from Eduardo Vargas before turning and firing a vicious volley beyond a helpless Fraser Forster.
Yet parity lasted just two minutes for QPR as Pelle bettered Austin's effort. The Italian flicked a seemingly innocuous ball up into the air and unleashed a superb overhead-kick that flew into the top corner.
Southampton's advantage came agonisingly close to being doubled in the 70th minute when Steven Davis curled an effort against the frame of the goal via the outstretched hand of Green.
Substitute Shane Long was then thwarted by Green in an effort to make the game safe and Southampton were almost punished for not doing so by Niko Kranjcar, who nearly replicated his heroics from last weekend’s 2-2 draw with Stoke City, his free-kick smashing the woodwork as the hosts clung on.