Eric Dier and Emmanuel Adebayor also scored in a convincing London derby win against the former Spurs boss.
Nacer Chadli opened the scoring after combining with Emmanuel Adebayor before Eric Dier scored his second goal in as many games on the half-hour mark.
Chadli bagged his second of the game before halftime and Adebayor converted a Ben Davies cross to wrap up the win after the break.
The result sees Tottenham maintain its winning start to the 2014-15 campaign, while QPR is left searching for its first points since returning to the top flight.
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Redknapp handed debuts to Mauricio Isla — on loan from Juventus — and Leroy Fer, who arrived from Norwich City earlier this week, while Erik Lamela made his first Premier League start at White Hart Lane, six days short of a year since he became Tottenham's record signing.
It was the home side that applied all of the pressure early — Adebayor nodding narrowly over from a Nabil Bentaleb cross — and it was not long before Spurs were in front.
Adebayor turned provider as he dinked a cross in from the left, and Chadli took the ball down wonderfully on his chest before poking it beyond Robert Green in the QPR net.
QPR was giving Tottenham far too much space, and Pochettino's men could have been further in front two minutes later had Adebayor capped off a swift counterattacking move with a better finish.
It was becoming clear that QPR would need to make the best of any opportunities that fell its way.
However, when Matt Phillips cut inside Younes Kaboul in the penalty area after meeting a long-range pass, he fluffed the finish by clearing the crossbar.
The visitors were very nearly punished moments later when Christian Eriksen rattled the crossbar from a 25-yard free kick, but Dier then powered home a header, leaving a glum-looking Redknapp scratching his head on the QPR bench.
Chadli doubled his tally seven minutes later, placing a header into the bottom-left corner from a chipped Lamela cross after a rampant Tottenham had strung together an incredible 48 passes in the buildup.
Steven Caulker got a rare glimpse at goal for QPR shortly after the break, but placed his header a yard wide of the right-hand post from a corner, before Adebayor slid the ball past Green for a fourth after being teed up by Danny Rose.
Rose almost gave QPR a hand nine minutes from time when he diverted the ball into his own net, but the referee disallowed the goal, leaving the visitors to mull over a dismal performance in which they rarely looked like troubling Tottenham goalkeeper Hugo Lloris.