The Moroccan's goalscoring intervention arrived in the 24th minute when he beat Spurs goal Brad Friedel from distance.
Spurs continued to dominate the encounter after the restart in terms of possession, but they very rarely called Kenny into any telling action.
Their best chance fell to Van der Vaart 20 minutes from time, but the Dutchman sent his effort from 18 yards out over the bar.
Having earlier given his side the lead, Taarabt left QPR to play the remaining 12 minutes a man light when he was handed a second caution from referee Mark Clattenberg for kicking the ball away after a foul had been given.
Despite their numerical disadvantage, QPR held out to lift themselves three points clear of the relegation zone.