Santa Cruz struck with 16 minutes remaining to settle a dour game which all but ended Pompey's faint hopes of snatching fifth place.
Portsmouth were rocked when goalkeeper David James was ruled out for the first time in 167 Premier League matches after suffering a torn calf.
Stand in keeper Jamie Ashdown almost endured a nightmare opening to his first league appearance in two years when he flapped at Santa Cruz's cross after just 11 minutes.
Ashdown was let off the hook when Morten Gamst Pedersen failed to get a proper connection on his header and nodded into the stands.
It took until the final six minutes of the first half for the match to spark into life, with both teams going close to opening the scoring in quick succession.
First Jermain Defoe thrashed a shot into the side-netting after a powerful solo run down the right wing.
Defoe was unlucky not to hit the target two minutes later when his low right-foot shot shaved Brad Friedel's upright after clever interplay between Nwankwo Kanu and John Utaka.
Ashdown was forced into his first meaningful save off the game soon after when he stood firm to palm away former Portsmouth loan striker Jason Roberts' 16-yard piledriver.
Portsmouth suffered another injury blow during the interval when Utaka limped off with a hamstring strain to be replaced by Croatia midfielder Niko Kranjcar.
Ashdown produced a superb fingertip save to deny Blackburn captain Ryan Nelsen a rare goal 13 minutes after the restart.
David Bentley dribbled the ball along Pompey's byline before crossing for the onrushing Nelson, whose diving header was brilliantly turned wide by Ashdown.
But Santa Cruz silenced the home fans by firing Blackburn in front with the 17th goal of his maiden Premier League season.
Ashdown punched the ball straight to Pedersen who picked out Santa Cruz on the edge of the penalty area and the Paraguayan played a neat one-two with strike-partner Roberts before calmly slotting past Ashdown from eight yards.