Rickie Lambert's first-half strike extended Southampton's lead at the top of the table to four points and dealt a blow to Leeds's play-off hopes.
Lambert put the visitors in front after quarter of an hour, smashing in a volley after Jack Cork's cross was nodded down by Tadanari Lee.
Leeds dominated for large parts of the game but failed to find an equaliser.
Saints keeper Kelvin Davis produced a string of fine saves in the second half and the home side twice hit the bar.
Davis was mobbed by his teammates after the final whistle, a testament to his inspired display, and the endeavour of the hosts who created numerous opportunities and will wonder how they ended up with nothing from the game.
The tone for what was to come was set in the fourth minute when Robert Snodgrass had a penalty appeal turned down after his shot hit the arm of Jose Fonte, while Davis smothered an Adam Clayton volley.
Leeds continued to press and only a smart block from Jos Hooiveld prevented Ross McCormack pouncing from two yards before, against the run of play, Lambert opened the scoring.
But the hosts continued to take the game to the league leaders undaunted, Snodgrass crossing for Ross McCormack, whose header was brilliantly kept out by Davis.
And as Leeds's barrage continued into the second half Davis continued to repel Neil Warnock's side with a stunning trio of saves in a mad five-minute period.
First, after failing to gather a cross, he scrambled back to somehow claw a Becchio effort off the line, then he twice denied impressive Leeds debutant Danny Webber.
In a late melee, Becchio and Darren O'Dea both headed against the bar before Tom Lees had a stinging shot blocked, and the spirited Saints held on to secure victory.