Polish striker Rasiak pounced after goalkeeper Simon Royce fumbled Gareth Bale's 80th-minute corner.
And substitute Wright-Phillips' injury-time strike sealed Rangers' seventh home defeat of the season.
The west London outfit, plagued by problems on and off the pitch, are now in grave danger of slipping into League One.
Southampton were by far the better team against a Rangers side without injured skipper Marcus Bignot and suspended winger Lee Cook.
The Saints had an early chance to go ahead when the hapless Royce twice was unable to gather Bale's free-kick, but Rasiak failed to take advantage, heading wide from six yards out.
Royce made amends by pushing away two efforts from Mario Licka - the first a right-footed shot from the edge of the penalty area, and the second a venomous drive that was heading towards the corner of the net.
Rangers were clearly struggling and suffered another setback when influential midfielder Marc Bircham was forced to go off injured.
Bircham's replacement, Stefan Bailey, created the home team's best moment of the first period. The teenager burst forward and slipped the ball through to Dexter Blackstock, who dragged his shot wide of the target.
Southampton continued to dominate after the break and Kenwyne Jones missed a golden chance to score when he headed Bale's free-kick just wide.
Jermaine Wright blasted over Royce's crossbar from 20 yards, before Rangers youngster Shabazz Baidoo was almost punished for a sloppy mistake.
Baidoo tried to play his way past Pele but was dispossessed by the midfielder, who let fly with a fierce shot that flew wide.
George Burley's men seemed in complete control, but survived a scare when they failed to deal with Jimmy Smith's corner and Blackstock's overhead kick was cleared off the line by Wright.
That galvanised QPR but Southampton responded by breaking the deadlock. Bale posed a threat from set-pieces all afternoon, and when his corner was spilled by Royce, Rasiak bundled the ball home.
Rangers thought they had equalised with a similar goal two minutes later, when keeper Kelvin Davis dropped Smith's corner and Blackstock turned the ball into the net.
But referee Trevor Kettle ruled that Davis had been fouled - much to the disgust of the home supporters.
And the R's fans' hopes of a point were well and truly crushed when Wright-Phillips latched onto David McGoldrick's throughball and fired past Royce with virtually the last kick of the match.