The home side had the first chance of the night less than 10 minutes after kickoff as John Swift tried to curl the ball in from the edge of the area, but Robert Green was left with a comfortable save.
Brentford continued to look the more likely in the early stages as Swift charged towards the QPR goal again before Jake Bidwell got the cross in for Alan McCormack, but the midfielder's header was high.
The visitors tried to create something down the other end as Matt Phillips delivered a long ball forward into the Brentford penalty area, but it was straight into the hands of the keeper, allowing the Bees to get back on the attack.
QPR were stretching the Brentford defence again shortly before half time though as Jay Emmanuel-Thomas set up Phillips but David Button made the save, while Tjaronn Chery fired over from another Emmanuel-Thomas delivery.
Both sides had chances to get a goal on the board as the half-time whistle neared, but Massimo Luongo was denied by the crossbar while attempting to head in from a Phillips cross, before thumping another effort against the post a couple of minutes later, while Green denied Alan Judge's 30-yard effort.