It was a rare Elland Road victory for the Saints who recovered from a slow start and finished well on top to condemn Dennis Wise to his first home defeat as Leeds manager.
Leeds, denied their first back-to-back league win since March, had David Healy back after suspension in the absence of the injured Richard Cresswell.
The Saints, who had failed to win on their last seven visits to Elland Road, were boosted by the return to fitness of Gareth Bale and Rasiak, who missed midweek international games for Wales and Poland respectively, but Kenwyne Jones and Inigo Idiakez were ruled out.
Leeds squandered two good chances in the opening seven minutes, Geoff Horsfield shooting wide of the near post and Matt Heath failing to control the ball when unmarked inside the six-yard box.
Bradley Wright-Phillips gave Leeds a scare with an accurate shot towards the far corner of the net but Graham Stack dived full length to his left to turn the ball away from its target.
There was ample entertainment and when Stephen Cainey, Hayden Foxe and Horsfield created an opening for Healy, the Northern Ireland international's rising shot was palmed over at full stretch by Saints keeper Kelvin Davis.
However, the Saints, who looked menacing on the counter-attack, took a 29th-minute lead. Highly-rated left-back Bale crossed for Andrew Surman to head towards the far post where Rasiak headed confidently past Stack for his ninth goal of the season and his first in nine games.
Leeds replaced the ineffective Horsfield with Ian Moore in the 55th minute and the substitute was only denied a rapid goal by the timely intervention of Saints skipper Claus Lundekvam who made a superb blocking tackle eight yards out.
The Saints were the more fluent side and deservedly scored again in the 69th minute.
John Viafara, the Saints' Colombian international, had replaced Wright-Phillips five minutes earlier, and when Leeds failed to cut out his low centre from the right, Skacel was unmarked at the far post to drill the ball into the net.
Six minutes later Rasiak headed his second and the Saints' third goal when he met Skacel's corner to punish more defensive slackness by the home team.