Two weeks after his sensational 55-yard strike against Chelsea, the midfielder fired home from much closer range six minutes from time to seal all three points for Mark Hughes' side at the Britannia Stadium.
Morgan Schneiderlin had given Southampton the lead midway through the first half after some questionable Stoke defending from a set-piece and Graziano Pelle could have doubled their advantage before the break.
Stoke were level minutes after the restart, though, as Mame Biram Diouf netted his ninth league goal of the season after Kelvin Davis had misjudged a Steven N'Zonzi cross.
With a point only enough to take them above Liverpool into fifth on goal difference, Southampton pushed for a later winner, but their efforts proved fruitless.
Instead, it was Stoke who made the breakthrough, Adam delivering a blow to Southampton's hopes of securing European football with a neat finish from 10 yards.
It was the hosts who began the brighter with Stephen Ireland and Diouf – two of Stoke's three changes - threatening in the final third, but there was no repeat of the dream start they enjoyed in this fixture last season, when goalkeeper Asmir Begovic scored with just 13 seconds gone.
The visitors – who welcomed back Dusan Tadic – slowly began to settle and Pelle went agonisingly close to breaking the deadlock after 16 minutes.
Sadio Mane spun away from Glenn Whelan 25 yards from goal and played a neat pass into the Italian striker, who controlled the ball perfectly only for his right-footed effort to ripple the side-netting.
Southampton did not have to wait long for the opening goal, though, as poor Stoke defending from a corner gifted Schneiderlin his fourth in the league this season after 22 minutes.
Sloppy marking allowed the Frenchman to ghost in unmarked at the back post to poke home, the 25-year-old tapping in Jose Fonte's front-post flick from a yard out.
Although Stoke continued to press, they lacked a real cutting edge and Hughes' side were nearly punished on the half hour as Pelle again found space, but his low effort was easily saved by Begovic.
Ronald Koeman's side saw their advantage disappear two minutes after the restart as Diouf dragged Stoke level, albeit in bizarre circumstances.
N'Zonzi's miscued cross looped over Kelvin Davis before striking the crossbar, the loose ball fell to Diouf and he had the simple task of firing into an unguarded net.
Having fought hard to restore parity a moment of madness from Begovic nearly saw Stoke fall behind again on the hour, the goalkeeper racing out to meet Mane on the right-edge of his penalty area.
The Senegal international turned away from Begovic and played a low centre to Tadic, but his effort was superbly kept out by Whelan on the line.
Adam - a half-time substitute - made Southampton rue that miss as he completed Stoke's second-half comeback, the Scot finding space inside a crowded penalty area to fire past Davis.
To add further disappointment to Southampton's day, defender Toby Alderweireld left the pitch on a stretcher in stoppage time with a shoulder injury.
