Wotton's powerful penalty six minutes from the end of a game - which kicked off 15 minutes late following a power cut at Home Park - lifted the Pilgrims further towards Coca-Cola Championship safety.
The captain converted after referee Andy Hall had controversially pointed to the spot for an infringement by centre-back Claus Lundekvam, but whether he had handled the ball or fouled Argyle striker Mickey Evans was unclear.
The Pilgrims had taken the lead on the stroke of half-time when Nick Chadwick had profited from some hesitancy in the defence to fire home a left-footed shot from the edge of the penalty area for his sixth goal of the season.
However, Southampton had the better of the second half and deservedly equalised when teenager Andrew Surman raced into the Argyle penalty area to head home Matt Oakley's long throw.
The introduction of substitute Bojan Djordjic turned the game Argyle's way after some enterprising play by Saints.
His play on the left turned the momentum towards the home team and led to the throw from which Saints conceded the match-winning penalty.
Wotton ignored some gamesmanship to send Argyle above Southampton into 14th place in the Championship - their highest league position since the opening week of the season.
Despite Wotton's goal leaving very little time for Saints to level, they were within inches of doing so through half-time substitute Kenwyne Jones.
Jones beat the Argyle defence to Oakley's floated free-kick and got a powerful head on the ball, but he was brilliantly thwarted by goalkeeper Romain Larrieu.