On an afternoon of few clear-cut chances, neither side could find the quality required in front of goal to turn one point into all three.
Both teams struggled to muster a serious attempt on target in an uneventful opening 45 minutes, with Badou Ndiaye's attempt down the middle for Alex McCarthy to keep out pretty much as good as things got.
That shot arrived just a few minutes in, and Ndiaye would squander a better opportunity later in the half when glancing Xherdan Shaqiri's shot wide of the target.
Kostas Stafylidis was next to try his luck, sending the ball high and wide following some nice interplay from City, as the two sides went into the break all square.
Stoke, who had the joint-worst away record in the division ahead of today's match, made a second change at the break as Peter Crouch - boasting four goals against his former club - came on for Stafylidis.
Half-time sub Crouch was making an impact, meanwhile, firing a volley over the crossbar and then flicking the ball on for Maxim Choupo-Moting, who could not keep his composure when through on goal.
Home boss Mauricio Pellegrino, who has now seen his side go eight home matches without a win, rolled the dice 25 minutes from time by bringing on Jese Rodriguez and Manolo Gabbiadini, the latter of whom ended a 16-game wait for a goal last time out.
The changes almost had an instant impact as, with their fans now firmly behind them, Cedric Soares put his foot through the ball from range and forced Butland into making a big stop.
Redmond sent in a delightful cross from the right and Boufal did the hard work by outjumping his man, only to send the resulting header wide of the target from eight yards on an afternoon when the ball did not ever look like ending up in the back of the net.
SOUTHAMPTON (4-3-3): McCarthy; Cedric, Stephens, Hoedt, Bertrand; Lemina, Romeu, Sims (Boufal 76'); Tadic (Gabbiadini 65'), Redmond, Carrillo (Long 79')
STOKE CITY (4-3-3): Butland; Bauer, Martins-Indi, Zouma, Stafylidis (Crouch 46'); Cameron, Ndiaye, Allen; Shaqiri, Diouf (Pieters 23'), Choupo-Moting (Jese 65')