Billy Jones' clinical finish fired Preston ahead in the 37th minute and fellow full-back Callum Davidson doubled the advantage from the penalty spot 11 minutes after the restart.
Yet Neil Warnock's men refused to lie down and on-loan Tottenham playmaker Taarabt, 20, capped an outstanding display with assists for both Rangers goals.
First the Moroccan played in right-back Peter Ramage to rifle home a fine finish in the 57th minute and another clever pass allowed Tamas Priskin to level the scores nine minutes later.
Rangers had chances to win the game that were spurned, with substitute Rowan Vine most culpable with a dreadful finish after Taarabt had played him in.
The opening half was largely devoid of inspiration and often resembled a meaningless end-of-season encounter.
But, in the 28th minute, QPR defender Kaspars Gorkss greeted Taarabt's inswinging corner with a firm header goalwards.
Preston striker Neil Mellor nodded the ball off the line and soon showed his quality at the other end of the field with a fine piece of skill to beat Gorkss down the right flank.
Mellor's low cross found Jon Parkin, who connected with a powerful right-foot shot that rebounded off a post.
Taarabt then showed some clever footwork inside the Preston penalty box to engineer the space for a low shot which Andy Lonergan did well to smother at his near post.
Eight minutes before the break, Preston forged ahead when Richard Chaplow's outswinging corner from the right fell to Jones, who took one touch to control the ball and another to fire high into the net from six yards.
The game looked all over 11 minutes after the break when Parkin was clumsily hauled to the ground by Gorkss and Davidson made no mistake from the spot with a thunderous left-foot strike into the top corner.
Yet Rangers hit back immediately when Taarabt spotted Ramage making progress inside the right channel and his perfect pass was met with a fierce first-time shot from the defender which flew into the far corner.
The goal poured belief into Warnock's players and they were level nine minutes later when another clever pass from Taarabt caused confusion in the home defence and allowed Priskin to fire home from the edge of the 18-yard box.
The goal followed a mix-up between home debutant Elliott Ward - who joined on loan from Coventry earlier in the week - and Lonergan.
Rangers began to dominate and pushed hard for a winner only to be denied by Lonergan and the wastefulness of Alejandro Faurlin and substitute Vine, who both blazed over the crossbar when well placed.
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