The Italy striker struck twice in the first 30 minutes and despite Marko Arnautovic reducing the arrears and Southampton substitute Sadio Mane seeing red at the death, Ronald Koeman’s side held on for victory.
In ending a three-game winless run in the Premier League, Southampton climbed above Mark Hughes' Stoke to seventh place, three points below Manchester United, who currently occupy the last Europa League slot.
It was Southampton’s first league win at the Britannia Stadium since April 2006.
Stoke welcomed captain Ryan Shawcross back after eight games out with a back problem and they made a positive start, Giannelli Imbula shooting wide after a positive run and Ibrahim Afellay seeing a shot blocked.
But no sooner had Southampton stirred as an attacking force, Stoke goalkeeper Jack Butland tipping Pelle’s header over the bar, than they went ahead.
From Steven Davis’ left-wing corner, Pelle rose at the near post to glance a header past Butland.
Butland parried from Shane Long shortly after, but on the half-hour the Stoke goalkeeper was at fault as Pelle swapped passes with Dusan Tadic before curling in a tame shot that the England international should have saved.
To make matters worse for the home side, winger Xherdan Shaqiri was then forced off holding the top of his thigh, with Bojan Krkic coming on.
Southampton squandered a gilt-edged chance to effectively kill the game off before half-time as Long freed Tadic, whose decision to cut inside onto his right foot allowed Geoff Cameron to come across and block.
Stoke sought to exploit the let-off and reduced the deficit in the 52nd minute, Arnautovic flicking the ball into the roof of the net from Afellay’s cross.
Stoke pushed for a leveller, but found no joy, Afellay shooting over from range and Virgil van Dijk brilliantly diverting Mame Biram Diouf’s shot over the bar.
Southampton should have been awarded a penalty when Tadic was sent sprawling by Butland after knocking the ball past him, only for referee Lee Mason to shake his head.
After Southampton substitute James Ward-Prowse had struck the bar with a free-kick, Mason angered the visitors again by showing Mane a straight red card for an aerial challenge on Erik Pieters, but Koeman’s men survived.
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