Rasiak pounced once in each half to take his personal tally for the season to 18 goals, one more than his previous best for Derby, and we are only just into January.
Young Torquay goalkeeper Martin Horsell had played well in the first half, pulling out one outstanding save from David McGoldrick after only 35 seconds.
But when he let the ball out of his grasp for a split second in the 43rd minute - he was worried about dragging it over his own by-line for a corner - Rasiak pounced and scored from a narrow angle.
Then, in the 72nd minute, substitute Mario Licka delivered a pinpoint right-wing cross for Rasiak to give Horsell no chance with a powerful near-post header.
Saints, who have now lost only once in 14 games, were too strong for a Torquay side which is six points adrift at the bottom of League Two.
McGoldrick, making a lively first start of the season, nearly scored early on and midfielder John Viafara was unlucky with several shots that were deflected wide.
Southampton even coped with the early loss of left-back Chris Makin, who had to go off after only 25 minutes with hamstring trouble. Martin Cranie, just back from a loan spell at Yeovil, took over in an already re-shuffled defence which featured the experienced Darren Powell in place of the injured Claus Lundekvam.
When Rasiak broke the deadlock, it merely confirmed Southampton's superiority, and it was 57 minutes before their goalkeeper Kelvin Davis had a shot on target to save, but Chris McPhee's weak effort caused no problem.
But Torquay were enjoying their best spell - Saints defender Pele just got back to deny Lee Thorpe and Steve Woods also headed an Adam Murray cross over - when Rasiak then made it 2-0.
Licka, who replaced Marcelo Sarmiento on the hour, enjoyed an impressive 30 minutes on Southampton's right wing, and his cross for Rasiak's thumping header was the highlight.
Despite some good work by Torquay's Murray in the boggy midfield, the match was over as a contest.
Torquay did miss two good chances in the last 10 minutes. Thorpe, with only Davis to beat, tried to lift the ball over the Saints keeper and shot wide, before Woods volleyed over from 10 yards from a Murray corner.
But Southampton never looked in danger of losing it, and their fine current run goes on.