The Italian striker scored twice in the first-half, finding the net after a long wait with a flicked header and a neat low finish.
It was game on early in the first-half when Marko Arnautovic pulled a goal back for hosts Stoke, but it wasn’t enough for Mark Hughes’ side.
Pelle opened the scoring after just 12 minutes, though his goal was cruel on young English goalkeeper Jack Butland.
The Stoke glovesman first denied Pelle with a brilliant one-handed save, as the striker’s thumping nodded effort looked destined for the top bin. But he was beaten from the following corner as Pelle ghosted in front of him and glanced a header into the net.
It was 2-0 on the half-hour mark, as Pelle latched onto Dusan Tadic’s cross to fire a low shot past Butland.
Tadic could have made it three and made the points safe before the break, but paid the price for his own hesitance.
He simply HAD to score after being played clean through, but he cut back on his favoured right foot and just took too long to let fly, allowing Geoff Cameron to fly in with a perfectly timed tackle.
Arnautovic gave Stoke hope of a comeback with a goal shortly after the re-start. A good move fed in Ibrahim Afellay on the left wing, and his cross was well met by the Austrian forward ,who slammed in at the near post.
Stoke came forward in search on the equaliser, but couldn’t find their way past the Saints’ solid back-four, with Virgil van Dijk proving a rock at the back.
Is was the Dutch centre-back’s brilliant last-gasp challenge which denied Mame Biram Diouf a chance from a wide open position, while Fraser Forster was forced into his first real save to palm away a strong Arnautovic drive.
But the Saints had their chances too, with James Ward-Prowse hitting the crossbar with a fine free-kick attempt.
Southampton found themselves down to ten men when substitute Sadio Mane was dismissed for an elbow in stoppage-time, but luckily for them it was too late for it to have an impact as the visitors held on.